Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsCombinatorics Seminar, Oct 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120268&date=2018-10-01
A cellular string of a polytope is a sequence of faces of the polytope that are stacked on top of each other in a particular direction. The collection of cellular strings, ordered by refinement, forms a poset that is homotopy equivalent to a sphere. Among the set of strings, the subposet of coherent ones is homeomorphic to a sphere. In this talk, I will give an oriented matroid characterization of zonotopes whose poset of cellular strings is a sphere, i.e. for which all strings are coherent. This is based on joint work with Rob Edman, Pakawut Jiradilok, and Gaku Liu.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120268&date=2018-10-01String-Math Seminar, Oct 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120355&date=2018-10-01
Several deep mathematical and physical results such as Kontsevich's deformation-quantization, Drinfeld's associators, and the Deligne hypothesis are controlled by the vanishing of certain obstruction classes in the theory of differential graded operads. I will talk about a way to obtain such vanishing results, as well as higher-genus analogues, using a weight theory implied by a new motivic point of view on the conformal operad.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120355&date=2018-10-01Northern California Symplectic Geometry Seminar, Oct 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120428&date=2018-10-01
See bulletin board for abstracts.<br />
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Please contact alanw@math.berkeley.edu to request or offer a ride for carpools leaving Evans Hall at 1:15 PM.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120428&date=2018-10-01Differential Geometry Seminar, Oct 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120228&date=2018-10-01
In the early 80's, Yau conjectured that in any closed $3$-manifold there should be infinitely many minimal surfaces. I will review previous contributions to the question and present a proof of the conjecture, which builds on min-max methods developed by F. C. Marques and A. Neves. A key step is the construction by min-max theory of a sequence of closed minimal surfaces in a manifold N with non-empty stable boundary, and I will explain how to achieve this via the construction of a non-compact cylindrical manifold.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120228&date=2018-10-01Arithmetic Geometry and Number Theory RTG Seminar, Oct 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120427&date=2018-10-01
Pre-talk: For a Galois representation of a number field arising from a smooth projective variety, the Weil conjecture tells that its Frobenius traces are rational numbers. Fontaine and Mazur conjectured that Galois representations satisfying a local condition (de Rham) arise from geometry and hence have a similar finiteness property of Frobenius traces. In the pretalk, I will explain these backgrounds.<br />
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Main talk: Etale local systems on an algebraic variety are a natural generalization of Galois representations of a filed. In the main talk, I will focus on de Rham local systems and explain a finiteness result on Frobenius traces follows from the Fontaine-Mazur conjecture for Galois representations and the generalized Riemann Hypothesis.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120427&date=2018-10-01Analysis and PDE Seminar, Oct 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120476&date=2018-10-01
The systems of coupled NLS equations occur in some physical problems, in particular in nonlinear optics (coupling between two optical waveguides, pulses or polarized components…). From the mathematical point of view, the coupling effects can lead to truly nonlinear behaviors, such as the beating effect (solutions with Fourier modes exchanging energy) of Grébert, Paturel and Thomann (2013). In this talk, I will use the coupling between two NLS equations on the 1D torus to construct a family of linearly unstable tori, and therefore unstable quasi-periodic solutions. The idea is to take profit of the Hamiltonian structure of the system via the construction of a Birkhoff normal form and the application of a KAM theorem. In particular, we will see of this surprising behavior (this is the first example of unstable tori for a 1D PDE) is strongly related to the existence of beating solutions.<br />
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This is a work in collaboration with Benoît Grébert.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120476&date=2018-10-01Seminar 217, Risk Management: Predicting Portfolio Return Volatility at Median Horizons, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118742&date=2018-10-02
Commercially available factor models provide good predictions of short-horizon (e.g. one day or one week) portfolio volatility, based on estimated portfolio factor loadings and responsive estimates of factor volatility. These predictions are of significant value to certain short-term investors, such as hedge funds. However, they provide limited guidance to long-term investors, such as Defined Benefit pension plans, individual owners of Defined Contribution pension plans, and insurance companies. Because return volatility is variable and mean-reverting, the square root rule for extrapolating short-term volatility predictions to medium-horizon (one year to five years) risk predictions systematically overstates (understates) medium-horizon risk when short-term volatility is high (low). In this paper, we propose a computationally feasible method for extrapolating to medium-horizon risk predictions in one-factor models that substantially outperforms the square root rule.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118742&date=2018-10-02Symplectic Working Group, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120543&date=2018-10-02
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120543&date=2018-10-023-Manifold Seminar, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120475&date=2018-10-02
We'll continue to discuss Thaddeus' proof that the trace of a simple closed curve is a perfect Morse function on the projective SU(2) representation variety of a surface.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120475&date=2018-10-02Probabilistic Operator Algebra Seminar, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119984&date=2018-10-02
One may think of an "independence relation" as a prescription for building joint distributions of (non-commutative) random variables, satisfying some nice universality properties. Work of Muraki and of Ben Ghorbal and Schurmann has shown that there are very few such universal independences; even with the fewest required "nice properties", there are no more than five. In this talk I will give an introduction to monotonic independence of random variables which fits in only the broadest category as it is not symmetric: $X$ being monotonically independent from $Y$ is \emph {not} equivalent to $Y$ being monotonically independent from $X$. Our goal will be to investigate the behaviour of additive monotonic convolution: given probability measures µ and ν, and random variables $X \sim \mu $ and $Y \sim \nu $ in some algebra where $X$ is monotonically indepenedent from $Y$, what is the distribution of $X+Y$? I will cover the analytic techniques necessary to answer this question, and in the time remaining, begin an investigation into monotone infinite divisibility and semigroups of convolution. This talk will draw material variously from papers of Muraki, of Bercovici and of Hasebe.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119984&date=2018-10-02The challenge of big data and data science for the social sciences, Oct 2
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120009&date=2018-10-02
The 2005 National Science Foundation workshop report on "Cyberinfrastructure for the Social and Behavioral Sciences" (Fran Berman and Henry Brady) argued that the methods of doing research in the social sciences would be transformed by big data and data science and that the social sciences should be centrally involved in studying the impacts of big data and data science on society. In "The Challenge of Big Data and Data Science," just completed for the Annual Review of Political Science, I have brought these arguments up-to-date. I will talk about defining "big data" and "data science," about the new kinds of research being done in the social sciences over the past decade that use big data and data science methods, and about the impacts of the information revolution on warfare, cities, the media, health care, and jobs and the ways that the social sciences must come to grips with them.<br />
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The Berkeley Distinguished Lectures in Data Science, co-hosted by the Berkeley Institute for Data Science (BIDS) and the Berkeley Division of Data Sciences, features Berkeley faculty doing visionary research that illustrates the character of the ongoing data revolution. This lecture series is offered to engage our diverse campus community and enrich active connections among colleagues. All campus community members are welcome and encouraged to attend. Arrive at 3:30 PM for light refreshments and discussion prior to the formal presentation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120009&date=2018-10-02Topology Seminar (Introductory Talk), Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120544&date=2018-10-03
In this introductory talk, we will discuss periodic dynamics on (punctured ) 2-torus, its algebraic incarnations, and its relations to dynamics on elliptic curves. In particular, we will give a geometric picture of how this could be used to distinguish total spaces of fibrations over tori/of analytic fibrations over elliptic curves. We will also try to demonstrate the periodic behavior of "flow lines" can survive in degenerate cases at an algebraic level.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120544&date=2018-10-03Concentration from Geometry in High Dimension, Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120103&date=2018-10-03
The concentration of Lipschitz functions around their expectation is a classical topic that continues to be very active. We will discuss some recent progress, including: <br />
1- A tight log-Sobolev inequality for isotropic logconcave densities<br />
2- A unified and improved large deviation inequality for convex bodies<br />
3- An extension of the above to Lipschitz functions (generalizing the Euclidean squared distance)<br />
The main technique of proof is a simple iteration (equivalently, a Martingale process) that gradually transforms any density into one with a Gaussian factor, for which isoperimetric inequalities are considerably easier to establish. The talk is joint work with Yin Tat Lee (UW) and will involve some elementary calculus.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120103&date=2018-10-03Number Theory Seminar, Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120426&date=2018-10-03
We will discuss the construction of $W\Omega _R^\ast $ and the comparison with the de Rham complex.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120426&date=2018-10-03Topology Seminar (Main Talk), Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120425&date=2018-10-03
One can construct the open symplectic mapping torus \(T_\phi \) for a given a Weinstein manifold \(M\) and a compactly supported symplectomorphism \(\phi \). Its contact boundary is independent of \(\phi \) and is equal to contact boundary of \(T_0\times M\) where \(T_0\) is the torus with a small ball removed. In this talk, we will outline a method to distinguish the fillings \(T_\phi \) and \(T_0\times M\). We will exploit the dynamics and deformation theory of the (wrapped) Fukaya categories, where the dynamics of the same sort is invisible at a geometric level.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120425&date=2018-10-03Statistical challenges in casualty estimation, Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120434&date=2018-10-03
An accurate understanding of the magnitude and dynamics of casualties during a conflict is important for a variety of reasons, including historical memory, retrospective policy analysis, and assigning culpability for human rights violations. However, during times of conflict and their aftermath, collecting a complete or representative sample of casualties can be difficult if not impossible. One solution is to apply population estimation methods-- sometimes called capture-recapture or multiple systems estimation-- to multiple incomplete lists of casualties to estimate the number of deaths not recorded on any of the lists. In this talk, I give an introduction to the procedures by which population estimation is performed in the context of conflict mortality, which mainly consists of a record linkage step followed by capture-recapture estimation. I then describe some of my recent work in this area, which is directed at elucidating the limitations of these statistical methods and proposing variants with better properties. I will conclude with a discussion of open questions in this challenging area of applied statistics.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120434&date=2018-10-03Representation Theory and Mathematical Physics Seminar, Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120542&date=2018-10-03
We propose a categorification of link invariants in Euclidean 3d space associated to a semi-simple Lie algebra, based on category of A-branes in finite dimensional Landau-Ginzburg (LG) models. The category of A-branes in such abstract LG model was constructed recently by Gaiotto, Moore and Witten; its mathematical counterpart is a version of Fukaya-Seidel category. The specific Landau-Ginzburg model needed is derived from string theory. We explain the relation to some other approaches to the same problem.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120542&date=2018-10-03Center for Computational Biology Seminar, Oct 3
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120220&date=2018-10-03
Title: Making sense of the “noise” in cancer data<br />
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During carcinogenesis, cells accumulate 1000s of somatic DNA mutations. “Driver” mutations bestow fitness advantages that lead to selective sweeps that increase that frequency of mutated cells compared to those lacking the driver. These sweeps also increase the frequency of “passenger” mutations accumulated since the last such sweep. These mutations have little impact on cell function but provide information about the mutational processes that generated them. Both their type (i.e., A to C) and genomic locations depend not only what caused the mutation -- e.g., UV light – but also the chromatin state of the cell that acquired it. My lab developed Bayesian inference methods to classify somatic mutations into different ‘subclones’ that correspond to different sweeps. Our methods also use phylogenetic approaches to determine the relative order in which the sweeps occurred. We are now developing supervised and unsupervised learning methods to interpret this historical record of the cancer, in order to use the timing and patterns of somatic mutations to reconstruct the changes that a normal cell underwent during its transformation into a cancerous cell.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120220&date=2018-10-03Applied Math Seminar, Oct 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120145&date=2018-10-04
In this talk, I begin wtih the nonlinear Schroedinger/Gross-Pitaevskii equations (NLSE/GPE) for modeling Bose-Einstein condensation (BEC), nonlinear optics, quantum physics and chemistry, etc., and review some dynamical properties of NLSE/GPE including conserved quantities, dispersion relation, center-of-mass dynamics, soliton solutions and semiclassical limits. Different numerical methods will be presented including finite different time domain (FDTD) methods and time-splitting spectral method, and their error estimates and comparison will be discussed. Extensions to NLSE/GPE with an angular momentum rotation term and/or non-local dipole-dipole interaction as well as multi-component will be presented. Finally, applications to soliton interactions, collapse and explosion of BEC, quantum transport and quantized vortex interaction will be investigated.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120145&date=2018-10-04Student Probability/PDE Seminar, Oct 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120267&date=2018-10-05
It is well-known that diffusions with gradient drifts exhibit metastable behavior. The large deviation estimates of Wentzel-Freidlin and classical Eyring-Kramers Formula give a precise description for such metastable behavior. For non-gradient models, the large-deviation techniques are still applicable, though no rigorous analog of Eyring-Kramers Formula is available. In this talk I give an overview of the existing results and conjectures for general metastable diffusions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120267&date=2018-10-05Combinatorics Seminar, Oct 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119664&date=2018-10-08
We study the Taylor expansion around the point $x=1$ of a classical modular form, the Jacobi theta constant $\theta_3$. This leads naturally to a new sequence $(d(n))^\infty_{n=0} =1,1,−1,51,849,−26199,\dots$ of integers, which arise as the Taylor coefficients in the expansion of a related "centered" version of $\theta_3$. We prove several results about the numbers $d(n)$ and conjecture that they satisfy the congruence $d(n)\cong (−1)^{n−1} (mod\, 5)$ and other similar congruence relations.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119664&date=2018-10-08String-Math Seminar, Oct 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120356&date=2018-10-08
A conjecture of Dunfield-Gukov-Rasmussen predicts a family of differentials on reduced HOMFLY-PT homology, indexed by the integers, that give rise to a corresponding family of reduced link homologies. We'll discuss a variant of this conjecture, constructing an unreduced link homology theory categorifying the quantum \(gl_n\) link invariant for all non-zero values of \(n\) (including negative values!). To do so, we employ the technique of annular evaluation, which uses categorical traces to define and characterize type A link homology theories in terms of simple data assigned to the unknot. Of particular interest is the case of negative n, which gives a categorification of the "symmetric webs" presentation of the type A Reshetikhin-Turaev invariant, and which produces novel categorifications thereof (i.e. distinct from the Khovanov-Rozansky theory).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120356&date=2018-10-08Differential Geometry Seminar, Oct 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120313&date=2018-10-08
We find a local solution to the Ricci flow equation under a negative lower bound for many known curvature conditions. The flow exists for a uniform amount of time, during which the curvature stays bounded below by a controllable negative number. The curvature conditions we consider include 2-non-negative and weakly $\mbox {PIC}_1$ cases, of which the results are new. We complete the discussion of the almost preservation problem by Bamler-Cabezas-Rivas-Wilking, and the 2-non-negative case generalizes a result in 3D by Simon-Topping to higher dimensions. As an application, we use the local Ricci flow to smooth a metric space which is the limit of a sequence of manifolds with the almost non-negative curvature conditions, and show that this limit space is bi-Hölder homeomorphic to a smooth manifold.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120313&date=2018-10-08Arithmetic Geometry and Number Theory RTG Seminar, Oct 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120674&date=2018-10-08
There is a canonical pairing on the Brauer group of a surface over a ﬁnite ﬁeld, and an old conjecture of Tate predicts that this pairing is alternating. In this talk I will present a resolution to Tate’s conjecture. The key new ingredient is a circle of ideas originating in algebraic topology, centered around the Steenrod operations. The talk will advertise these new tools (while assuming minimal background in algebraic topology).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120674&date=2018-10-08Seminar 217, Risk Management: Robust Learning: Information Theory and Algorithms, Oct 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118749&date=2018-10-09
This talk will provide an overview of recent results in high-dimensional robust estimation. The key question is the following: given a dataset, some fraction of which consists of arbitrary outliers, what can be learned about the non-outlying points? This is a classical question going back at least to Tukey (1960). However, this question has recently received renewed interest for a combination of reasons. First, many of the older results do not give meaningful error bounds in high dimensions (for instance, the error often includes an implicit sqrt(d)-factor in d dimensions). Second, recent connections have been established between robust estimation and other problems such as clustering and learning of stochastic block models. Currently, the best known results for clustering mixtures of Gaussians are via these robust estimation techniques. Finally, high-dimensional biological datasets with structured outliers such as batch effects, together with security concerns for machine learning systems, motivate the study of robustness to worst-case outliers from an applied direction.<br />
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The talk will cover both information-theoretic and algorithmic techniques in robust estimation, aiming to give an accessible introduction. We will start by reviewing the 1-dimensional case, and show that many natural estimators break down in higher dimensions. Then we will give a simple argument that robust estimation is information-theoretically possible. Finally, we will show that under stronger assumptions we can perform robust estimation efficiently, via a "dual coupling" inequality that is reminiscent of matrix concentration inequalities.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118749&date=2018-10-09Symplectic Working Group, Oct 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120632&date=2018-10-09
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120632&date=2018-10-09Probabilistic Operator Algebra Seminar, Oct 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120726&date=2018-10-09
The lattice of non-crossing partitions plays a crucial role in free probability, giving rise to the free cumulants introduced by Roland Speicher. In addition to their combinatorial description, the non-crossing partitions can be realized as arising from the Coxeter groups of Type A. Reiner used this analogy to introduce the non-crossing partitions of Type B, which raises the question: what do these correspond to on the non-commutative probability side ? It turns out that the Type B theory leads to a kind of infinitesimal free independence. In this expository talk, we will present these ideas and discuss (briefly) how they can be applied to understand finite rank perturbations of random matrices.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120726&date=2018-10-09Letters of recommendation in Berkeley undergraduate admissions: Program evaluation and natural language processing, Oct 9
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120051&date=2018-10-09
In Fall 2015 and 2016, UC Berkeley asked many freshman applicants to submit letters of recommendation as part of their applications. This was highly controversial. Proponents argued that letters would aid in the identification of disadvantaged students who had overcome obstacles that were not otherwise apparent from their applications, while opponents argued that disadvantaged students were unlikely to have access to adults who could write strong letters. I oversaw an experiment in the 2016-17 admissions cycle in which applications were scored with and without their letters. Initial analysis of the experiment indicated that when available the letters modestly improved the reader scores of students from underrepresented groups, and that few otherwise admissible students failed to submit letters when asked. I will also present results of a textual analysis of the letters themselves, using natural language processing to measure differences in the letters that underrepresented students receive compared to otherwise similarly qualified students not from underrepresented groups.<br />
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The Berkeley Distinguished Lectures in Data Science, co-hosted by the Berkeley Institute for Data Science (BIDS) and the Berkeley Division of Data Sciences, features Berkeley faculty doing visionary research that illustrates the character of the ongoing data revolution. This lecture series is offered to engage our diverse campus community and enrich active connections among colleagues. All campus community members are welcome and encouraged to attend. Arrive at 3:30 PM for light refreshments and discussion prior to the formal presentation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120051&date=2018-10-09Topology Seminar (Introductory Talk), Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120677&date=2018-10-10
Starting with closed symplectic manifolds, we introduce Hamiltonian Floer homology and discuss the dynamical information it encodes. We then translate this story to open symplectic manifolds, on which symplectic cohomology is defined.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120677&date=2018-10-10Bay Area Microlocal Analysis Seminar, Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120503&date=2018-10-10
We study the trapped set of spacetimes whose metric decays to a stationary Kerr metric at an inverse polynomial rate. In the first part of the talk, I will focus on the dynamical aspects of this problem and show that the trapped set is a smooth submanifold which converges to that of the stationary metric at the same rate. In the second part, I will explain how to use this to prove microlocal estimates at the trapped set for solutions of wave equations on such spacetimes.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120503&date=2018-10-10Large deviations of subgraph counts for sparse Erd\H{o}s--R\'enyi graphs, Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120664&date=2018-10-10
For each fixed integer $\ell\ge 3$ we establish the leading order of the exponential rate function for the probability that the number of cycles of length $\ell$ in the Erd\H{o}s--R\'enyi graph $G(N,p)$ exceeds its expectation by a constant factor, assuming $N^{-1/2}\ll p\ll 1$ (up to log corrections) when $\ell\ge 4$, and $N^{-1/3}\ll p\ll 1$ in the case of triangles. We additionally obtain the upper tail for general subgraph counts, as well as the lower tail for counts of seminorming graphs, in narrower ranges of sparsity. As in other recent works on the emerging theory of nonlinear large deviations, our general approach applies to functions on product spaces which are of ``low complexity", though the notion of complexity used here is somewhat different. Based on joint work with Amir Dembo.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120664&date=2018-10-10Number Theory Seminar, Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120633&date=2018-10-10
We will discuss the classical de Rham Witt complex and Zariski localization.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120633&date=2018-10-10To persist or not to persist?, Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120151&date=2018-10-10
Two long standing, fundamental questions in biology are "Under what conditions do populations persist or go extinct? When do interacting species coexist?" The answers to these questions are essential for guiding conservation efforts and identifying mechanisms that maintain biodiversity. Mathematical models play an important role in identifying these mechanisms and, when coupled with empirical work, can determine whether or not a given mechanism is operating in a specific population or community. For over a century, nonlinear difference and differential equations have been used to identify these mechanisms. These models, however, fail to account for stochastic fluctuations in environmental conditions such as temperature and precipitation. In this talk, I present theorems about persistence, coexistence, and extinction for stochastic difference equations that account for species interactions, population structure, and environmental fluctuations. The theorems will be illustrated with models of Bay checkerspot butterflies, spatially structured acorn woodpecker populations, competition among Kansas prairie grass species, and the evolutionary game of rock, paper, and scissors. This work is in collaboration with Michel Benaim.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120151&date=2018-10-10Bay Area Microlocal Analysis Seminar, Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120504&date=2018-10-10
I will show a frequency-independent lower bound on mass of eigenfunctions on surfaces of variable negative curvature. This was previously done in the case of constant curvature in joint work with Jin, relying on the fractal uncertainty principle proved in joint work with Bourgain. I will focus on the new components needed to handle the case of variable curvature, in particular propagation of quantum observables up to local Ehrenfest time. Joint work in progress with Long Jin and Stéphane Nonnenmacher.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120504&date=2018-10-10Topology Seminar (Main Talk), Oct 10
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120678&date=2018-10-10
Mirror symmetry predicts the existence of Floer invariants that yield “local” information. Guided by this, we construct a quantitative symplectic cohomology theory that detects Floer-essential Lagrangians within subdomains. We illustrate the quantitative behavior of this theory by examining negative line bundles over toric symplectic manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120678&date=2018-10-10Applied Math Seminar, Oct 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119846&date=2018-10-11
This talk will address the issue of closure in reduced order models (ROMs) and large eddy simulations (LES), leveraging ideas from non-equilibrium statistical mechanics. The approach is based on the Variational Multi-Scale method (VMS) and the Mori-Zwanzig (M-Z) formalism, which provides a framework to perform formal scale separation and re-cast a high-dimensional dynamical system into an equivalent, lower-dimensional system. In this reduced system, which is in the form of a generalized Langevin equation (GLE), the effect of the unresolved modes on the resolved modes appears as a convolution integral (which is sometimes referred to as memory). The M-Z formalism alone does not lead to a reduction in computational complexity as it requires the solution of the orthogonal dynamics PDE. A model for the memory is constructed by assuming that memory effects have a finite temporal support and by exploiting scale similarity. We discover that unresolved scales lead to memory effects that are driven by an orthogonal projection of the coarse-scale residual and inter-element jumps (in the case of discontinuous finite elements). It is further shown that an MZ-based finite memory model is a variant of the well-known adjoint-stabilization method. For hyperbolic equations, this stabilization is shown to have the form of an artificial viscosity term. We further establish connections between the memory kernel and approximate Riemann solvers. In the context of ROMs, this model is shown to yield a Petrov-Galerkin projection. Several applications in ROMs and LES ranging from simple scalar PDEs to Magneto-hydro-dynamic turbulence will be presented.<br />
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Bio: Karthik Duraisamy is an Associate Professor of Aerospace Engineering at the University of Michigan, Ann Arbor. He obtained a doctorate in aerospace engineering and masters in applied mathematics from the University of Maryland, College Park. He is the director of the Center for Data-driven Computational Physics and the associate director of the Michigan Institute of Computational Discovery and Engineering (MICDE) at the Univ of Michigan. His research interests are in data-driven and reduced order modeling, turbulence modeling and simulations, and numerical methods for PDEs.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119846&date=2018-10-11Mathematics Department Colloquium, Oct 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120272&date=2018-10-11
(joint with B.Bakker and Y.Brunebarbe) One very fruitful way of studying complex algebraic varieties is by forgetting the underlying algebraic structure, and just thinking of them as complex analytic spaces. To this end, it is a natural and fruitful question to ask how much the complex analytic structure remembers. One very prominent result is Chows theorem, stating that any closed analytic subspace of projective space is in fact algebraic. One notable consequence of this result is that a compact complex analytic space admits at most 1 algebraic structure - a result which is false in the non-compact case. This was generalized and extended by Serre in his famous GAGA paper using the language of cohomology.<br />
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We explain how we can extend Chow's theorem and in fact all of GAGA to the non-compact case by working with complex analytic structures that are "tame" in the precise sense defined by o-minimality. This leads to some very general "algebraization" theorems, and we give applications to Hodge theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120272&date=2018-10-11Student Probability/PDE Seminar, Oct 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120673&date=2018-10-12
We shall first recall how to obtain macroscopic PDEs by taking limits of Hamiltonian dynamics as the number of molecules increases to infinity. We shall then construct along these lines explicit examples of spontaneous energy generation (and therefore establish non-uniqueness) for the compressible Euler system, with and without pressure. The examples come from rescalings of well-posed deterministic systems of molecules that either collide elastically or interact via singular pair potentials. They live in space dimension 1 for the Euler with pressure and in higher dimensions, but have singular support, for the pressureless Euler. (Work with Jianfei Xue.)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120673&date=2018-10-12Logic Colloquium, Oct 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120271&date=2018-10-12
One of the goals of proof theory is to find combinatorial characterization of sentences provable in particular theories, i.e., to present these sentences as mathematical principles, rather than mere syntactical statements. While for strong theories these sentences tend to be incomprehensible, for weak theories we expect to find something familiar, or at least similar to well-known principles. In this talk I will report on the project to characterize provably disjoint NP pairs of sets in systems called Bounded depth Frege systems. The resulting characterization is expressed in terms of positional strategies in some combinatorial games that generalize the standard concept of a finite game.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120271&date=2018-10-12Combinatorics Seminar, Oct 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120269&date=2018-10-15
Many questions in combinatorics, probability and statistical mechanics can be reduced to counting lattice paths (walks) in regions of the plane. A standard approach to counting problems is to consider properties of the associated generating function. These functions have long been well understood for walks in the full plane and in a half plane. Recently much attention has focused on walks in the first quadrant of the plane and has now resulted in a complete characterization of those walks whose generating functions are algebraic, holonomic (solutions of linear differential equations) or at least differentially algebraic (solutions of algebraic differential equations). I will give an introduction to this topic, discuss previous work of Bousquet-Melou, Kauers, Mishna, and others and then present recent work by Dreyfus, Hardouin, Roques and myself applying the theory of QRT maps and Galois theory of difference equations to determine which generating functions satisfy differential equations and which do not.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120269&date=2018-10-15String-Math Seminar, Oct 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120725&date=2018-10-15
A conjecture of Gorsky-Negut-Rasmussen asserts the existence of a pair of adjoint functors relating the Hecke category for symmetric groups and the Hilbert scheme of points in the plane. One topological consequence of this conjecture is the prediction of a deformation of the triply graded Khovanov-Rozansky link homology which restores the missing \(q\rightarrow tq^{-1}\) symmetry of KR homology for links. In this talk I will discuss a candidate for such a deformation, constructed in joint work with Eugene Gorsky, which indeed facilitates connections with Hilbert schemes. For instance our main result explicitly computes the homologies (both deformed and undeformed) of the \((n,nk)\) torus links, summed over all \(n\geq 0\), as a graded algebra. Combining with work of Haiman this gives a functor from the Hecke category to sheaves on the relevant Hilbert scheme.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120725&date=2018-10-15Differential Geometry Seminar, Oct 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120505&date=2018-10-15
This is joint work with M. Eichmair and V. Moraru. We prove that if a 3-manifold with non-negative scalar curvature contains an absolutely area-minimizing cylinder then the ambient manifold is flat. This can be seen as a scalar curvature analogue of the Cheeger–Gromoll splitting theorem for Ricci curvature.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120505&date=2018-10-15Arithmetic Geometry and Number Theory RTG Seminar, Oct 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120840&date=2018-10-15
The local (and global) Langlands conjectures attempt to bridge the major areas of harmonic analysis and number theory by forming a correspondence between representations which naturally appear in both areas. A key insight due to Langlands and Kottwitz is that one could attempt to understand such a conjectural correspondence by comparing the traces of natural operators on both sides of the bridge. Moreover, it was realized that Shimura varieties present a natural means of doing this. For global applications, questions of reduction type (at a particular prime $p$) for these Shimura varieties can often be avoided, and for this reason the methods of Langlands and Kottwitz focused largely on the setting of good reduction. But, for local applications dealing with the case of bad reduction is key. The setting of bad reduction was first dealt with, for some simple Shimura varieties. Harris and Taylor then used this, together with the work of many other mathematicians, to prove the local Langlands conjecture for $GL_n$. A decade later Scholze gave an alternative, more geometric, way to understand the case of bad reduction for certain Shimura varieties and was able to reprove the local Langlands conjecture for $GL_n$ in simpler terms. In this talk we will discuss an extension of the ideas of Scholze to a wider class of Shimura varieties, as well as the intended application of these ideas to the local Langlands conjectures for more general groups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120840&date=2018-10-15Analysis and PDE Seminar, Oct 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120836&date=2018-10-15
In this talk, I will discuss the differential equation $iu_t = Hu, H := H_0 + V$ , where $V$ is a decaying potential and $H_0$ is a Laplacian related operator. In particular, I will focus on when $H_0$ is Laplacian, Bilaplacian and Dirac operators. I will discuss how the threshold energy obstructions, eigenvalues and resonances, effect the $L^1 \to L^\infty $ behavior of $e^{itH} P_{ac} (H)$. The threshold obstructions are known as the distributional solutions of $H\psi = 0$ in certain dimension dependent spaces. Due to its unwanted effects on the dispersive estimates, its absence have been assumed in many work. I will mention our previous results on Dirac operator and recent results on Bilaplacian operator under different assumptions on threshold energy obstructions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120836&date=2018-10-15Deformation Theory Seminar, Oct 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120824&date=2018-10-15
Let $A$ be an algebra. The Koszul duality is a type of derived equivalence between modules over $A$ and modules over its Koszul dual $A^!$. In this talk, we will talk about the general framework and then focus on the classical cases as well as examples.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120824&date=2018-10-15Representation theory seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120838&date=2018-10-16
Khovanov and Rozansky defined a link invariant called triply graded homology. It is conjectured by Gorsky, Negut and Rasmussen that this invariant can be expressed geometrically by a functor from complexes of Soergel bimodules to the derived category of coherent sheaves on the dg flag Hilbert scheme followed by taking cohomology. A functor with similar properties has been constructed by Oblomkov and Rozansky using matrix factorizations and it is believed that this functor solves the conjecture. The aim of this joint work in progress with Roman Bezrukavnikov is to relate the two constructions using previous work of Arkhipov and Kanstrup.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120838&date=2018-10-16Seminar 217, Risk Management: Asymptotic Spectral Analysis of Markov Chains with Rare Transitions: A Graph-Algorithmic Approach, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118748&date=2018-10-16
Parameter-dependent Markov chains with exponentially small transition rates arise in modeling complex systems in physics, chemistry, and biology. Such processes often manifest metastability, and the spectral properties of the generators largely govern their long-term dynamics. In this work, we propose a constructive graph-algorithmic approach to computing the asymptotic estimates of eigenvalues and eigenvectors of the generator. In particular, we introduce the concepts of the hierarchy of Typical Transition Graphs and the associated sequence of Characteristic Timescales. Typical Transition Graphs can be viewed as a unification of Wentzell’s hierarchy of optimal W-graphs and Friedlin’s hierarchy of Markov chains, and they are capable of describing typical escapes from metastable classes as well as cyclic behaviors within metastable classes, for both reversible and irreversible processes. We apply the proposed approach to conduct zero-temperature asymptotic analysis of the stochastic network representing the energy landscape of the Lennard-Jones cluster of 75 atoms.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118748&date=2018-10-163-Manifold Seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120839&date=2018-10-16
Bass-Serre theory studies groups acting on trees. The action of a group on a tree determines a quotient "graph of groups", from which one can reconstruct the original group via amalgamated free products and HNN extensions. We will study the tree associated to $PSL(2,{\mathbb Q}_p)$ in detail, discuss various higher-dimensional generalizations, and describe some applications to the study of incompressible surfaces in 3-manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120839&date=2018-10-16Student Harmonic Analysis and PDE Seminar (HADES), Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120842&date=2018-10-16
I will present the method introduced by András Vasy to prove meromorphic continuations of resolvents of Laplacians on asymptotically hyperbolic spaces in a simple model case. In particular, I will show the proof of Melrose's radial estimates indicating the idea behind the general case.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120842&date=2018-10-16Probabilistic Operator Algebra Seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120579&date=2018-10-16
With the introduction of free independence by D.V. Voiculescu, it became clear that in the framework of non-commutative probability there are other notions of independence than that of classical independence. The Boolean convolution between measures was formally introduced by Speicher and R. Woroudi in 1993, although it had previously appeared in the literature in different contexts, for example, as partial cumulants in stochastic differential equations. Later, in 2006, H. Bercovici provided the product for Hilbert spaces that, in the context of operator algebras, corresponds to the Boolean convolution between measures. In this talk we will survey the basics of Boolean probability, scenarios in which it appears naturally, together with some results that show the similarities and differences it has with the classical theory of probability.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120579&date=2018-10-16Topology Seminar (Introductory Talk), Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120679&date=2018-10-17
Random curves in space and how they are knotted give an insight into the behavior of "typical" knots and links. They have been studied by biologists and physicists in the context of the structure of random polymers. Several randomized models have been suggested and investigated both by theoretical methods and computational experiments. We will review some known and new models of random knotting, and will discuss their nature and the typical properties of the knots they produce.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120679&date=2018-10-17The Lovász theta function for random regular graphs, Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120791&date=2018-10-17
The Lovász theta function is a classic semidefinite relaxation of graph coloring. In this talk I'll discuss the power of this relaxation for refuting colorability of uniformly random degree-regular graphs, as well as for distinguishing this distribution from one with a `planted' disassoratative community structure. We will see that the behavior of this refutation scheme is consistent with the conjecture that coloring and community detection exhibit a `computationally hard but information-theoretically feasible' regime typical of random constraint satisfaction and statistical inference problems. The proofs will make use of orthogonal polynomials, nonbacktracking walks, and results on the spectra of random regular graphs.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120791&date=2018-10-17Number Theory Seminar, Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120727&date=2018-10-17
We will discuss étale localization in the theory of the de Rham Witt complex.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120727&date=2018-10-17Topology Seminar (Main Talk), Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120680&date=2018-10-17
The study of knots and links from a probabilistic viewpoint provides insight into the behavior of "typical" knots, and arises also in applications to the natural sciences. We will discuss knots that arise from random permutations using petal projections (Adams et al. 2012). We will explain why the probability of obtaining any given knot type in this model is positive if the number of petals is at least linear in the knot's crossing number, and why it decays to zero as this number grows to infinity. Our approach uses different knot invariants and arguments than those that have been used in other random models.<br />
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Joint work with Joel Hass, Nati Linial, and Tahl Nowik.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120680&date=2018-10-17Learning in Google Ads, Machines and People, Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120789&date=2018-10-17
This talk is in two parts, both of which discuss interesting uses of experiments in Google search ads. In part 1 I discuss how we can inject randomness into our system to get causal inference in a machine learning setting. In part 2. I talk about experiment designs to measure how users learn in response to ads on Google.com.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120789&date=2018-10-17Horizons in Quantum Computing, Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120910&date=2018-10-17
Quantum computing has seen enormous advancements in recent years, and lots of talent has been flowing into the field. With large companies like @IBM and secretive startups such as PsiQuantum disrupting the field, it is only a matter of time until we reach quantum supremacy.<br />
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But what will happen when quantum computers are powerful enough to break encryption or help reduce greenhouse gas emissions? What will be the benefits and downsides?<br />
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To answer such questions, we have invited four experts from the field to Berkeley. They will be debating when we will have powerful quantum computers and what we can expect from them. <br />
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Join us for our first annual quantum computing panel at Berkeley and connect with professionals from the field over food and refreshments.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120910&date=2018-10-17Applied Math Seminar, Oct 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120675&date=2018-10-18
Electronic correlation effects play an import role in emergent phenomena such as Mott-insulator-metal transition and unconventional superconductivity. Understanding these effects present a theoretical challenge. In this talk, we will give an overview of dynamical mean-field theory (DMFT) and its combination with the local density approximation in density functional theory. Representative quantum impurity solvers including continuous-time quantum Monte Carlo method will also be discussed, together with a few measurable quantities. Finally, I will present applications of the theoretical approach to strongly correlated f-electron systems.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120675&date=2018-10-18Mathematics Department Colloquium, Oct 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120841&date=2018-10-18
This is a joint work with Piermarco Cannarsa and Wei Cheng. <br />
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If A is a closed subset of the Euclidean space $R^k$, the Euclidean distance function $d_A : R^k \to [0, + \infty[$ is defined by<br />
<br />
$$d_A(x) = \mathrm{min}_{a \in A} ||x − a||.$$<br />
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This function is Lipschitz, therefore differentiable almost everywhere. We will give topological properties of the set Sing(F) of points in $R^k \setminus M$ where F is not differentiable. For example it is locally connected. We will also discuss the homotopy type of Sing(F).<br />
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Although, we will concentrate on $d_A$, we will explain that it is a particular case of a more general result on the singularities of a viscosity solution $F:R^k × ]0, +\infty[ \to R$ of the evolution Hamilton-Jacobi equation<br />
<br />
$$ \partial_t F + H(x, \partial_x F) = 0,$$<br />
<br />
where $H : R^k × R^k \to R$, $(x, p) \mapsto H(x, p)$ is a $C^2$ Tonelli Hamiltonian, i.e. convex and superlinear in the momentum p. If time permits we will explain the methods of proof for the case of $d_A$.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120841&date=2018-10-184th Annual CDAR Symposium 2018, Oct 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119719&date=2018-10-19
The fourth annual CDAR Symposium, presented in partnership with State Street, will convene on Friday, October 19, 2018, from 8:30 am to 6:30 pm at UC Berkeley’s Memorial Stadium. Our conference will feature new developments in data science, highlighting applications to finance and risk management. Confirmed speakers include Jeff Bohn, Olivier Ledoit, Ulrike Malmendier, Steven Kou, Ezra Nahum, Roy Henriksson, and Ken Kroner.<br />
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The Consortium for Data Analytics in Risk (CDAR) supports research into innovation in data science and its applications to portfolio management and investment risk. Based in the Economics and Statistics Departments at UC Berkeley, CDAR was co-founded with State Street, Stanford, Berkeley Institute for Data Science (BIDS), and Southwestern University of Finance and Economics (SWUFE). This year, CDAR welcomes a new founding member, Swiss Re based in Switzerland, and a new industry partner, AXA Rosenberg. CDAR organizes conferences, workshops, and research programs, bringing together academic researchers from the physical and social sciences, and industry researchers from financial management firms and technology development companies large and small.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119719&date=2018-10-19Student Probability/PDE Seminar, Oct 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120837&date=2018-10-19
We shall first recall how to obtain macroscopic PDEs by taking limits of Hamiltonian dynamics as the number of molecules increases to infinity. We shall then construct along these lines explicit examples of spontaneous energy generation (and therefore establish non-uniqueness) for the compressible Euler system, with and without pressure. The examples come from rescalings of well-posed deterministic systems of molecules that either collide elastically or interact via singular pair potentials. They live in space dimension 1 for the Euler with pressure and in higher dimensions, but have singular support, for the pressureless Euler. (Work with Jianfei Xue.)http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120837&date=2018-10-19Combinatorics Seminar, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120823&date=2018-10-22
A Hopf monoid is an algebraic structure that many families of combinatorial objects share. The collection of multiplicative functions defined on a Hopf monoid forms a group, called the character group. Aguiar and Ardila (2017) proved that the character groups for the Hopf monoids of permutahedra and associahedra are exponential power series under multiplication and composition, respectively. In this talk I will introduce the Hopf monoid of orbit polytopes, and then I will discuss some of my recent work on determining the structure of the character group of this Hopf monoid.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120823&date=2018-10-22String-Math Seminar, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120980&date=2018-10-22
I will describe a construction which, for a given \(4d\), \(N=2\) Argyres-Douglas SCFT, seems to produce a three-dimensional TQFT, whose underlying modular tensor category coincides with that of a \(2d\) chiral algebra of the parent \(4d\), \(N=2\) theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120980&date=2018-10-22Arithmetic Geometry and Number Theory RTG Seminar, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120940&date=2018-10-22
Shimura varieties attached to unitary similitude groups are a well-studied class of PEL Shimura varieties (i.e., varieties admitting a moduli description in terms of abelian varieties endowed with a polarization, endomorphisms, and a level structure). There are also natural Shimura varieties attached to (honest) unitary groups; these lack a moduli interpretation, but they have other advantages (e.g., they give rise to interesting cycles of the sort that appear in the arithmetic Gan-Gross-Prasad conjecture). I will describe some variant Shimura varieties which enjoy good properties from both of these classes. This is joint work with M. Rapoport and W. Zhang.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120940&date=2018-10-22Differential Geometry Seminar, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120724&date=2018-10-22
The notion of a harmonic Z/2 spinor was introduced by Taubes as an abstraction of various limiting objects appearing in compactifications of gauge-theoretic moduli spaces. I will explain this notion and discuss an existence result for harmonic Z/2 spinors on three-manifolds. The proof uses a wall-crossing formula for solutions of generalized Seiberg-Witten equations in dimension three, a result itself motivated by Yang-Mills theory on Riemannian manifolds with special holonomy $G_2$. The talk is based on joint work with Thomas Walpuski.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120724&date=2018-10-22Mathematical Theories of Communication: Old and New, Oct 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120115&date=2018-10-22
Reliable and efficient digital communication is possible today largely due to some wonderful successes in mathematical modelling and analysis. A legendary figure in this space is Claude Shannon (1916-2001) who laid out the mathematical foundations of communication in his seminal 1948 treatise, where among other contributions he gave a mathematical definition of "entropy" and coined the now ubiquitous term "bit" (for binary digit). But Shannon's theory is not the last word in communication. Communication extends to settings well beyond the carefully designed full information exchange model explored in Shannon's work. In this talk I will try to describe some of the many extensions that have been explored in the interim period including communication complexity (Yao 1980) that explores how it might be possible to achieve effective communication without a full exchange; interactive communication (Schulman 1992) which explores how to cope with errors in an interactive setting, and some of our own work on uncertain communication, which explores how shared context can make communication more effective, even if the context is shared only loosely.<br />
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Light refreshments will be served before the lecture at 3:30 p.m.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120115&date=2018-10-22Seminar 217, Risk Management: Proliferation of Anomalies and Zoo of Factors – What does the Hansen–Jagannathan Distance Tell Us?, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118743&date=2018-10-23
Recent research finds that prominent asset pricing models have mixed success in evaluating the cross-section of anomalies, which highlights proliferation of anomalies and zoo of factors. In this paper, I investigate that how is the relative pricing performance of these models to explain anomalies, when comparing their misspecification errors– the Hansen–Jagannathan (HJ) distance measure. I find that a traded-factor model dominates others in a specific anomaly by incorporating the multiple HJ distance comparing inference. However, different from the current research of Barillas and Shanken (2017) and Barillas, Kan, Robotti and Shanken (2018), I result that the HJ distance is a general statistic measure to compare models and some model-derived non-traded factors even outperform traded factors. Second, there is a large variation in the shape and curvature of these confidence sets of anomalies, which makes any single SDF difficult to satisfy confidence sets of anomalies all. My results imply that further work is required not only in pruning the number of priced factors but also in building models that explain the anomalies better.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=118743&date=2018-10-23Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119669&date=2018-10-23
The uniform probability measure on a convex polytope induces piecewise polynomial densities on the projections of that polytope. For a fixed combinatorial type of simplicial polytopes, the moments of these measures are rational functions in the vertex coordinates. We study projective varieties that are parametrized by finite collections of such rational functions. Our focus lies on determining the prime ideals of these moment varieties. Special cases include Hankel determinantal ideals for polytopal splines on line segments, and the relations among multisymmetric functions given by the cumulants of a simplex. In general, our moment varieties are more complicated, and they offer nice challenges for both numerical and symbolic computing in algebraic geometry. This is joint work with Kathlen Kohn and Boris Shapiro.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119669&date=2018-10-23Probabilistic Operator Algebra Seminar, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120169&date=2018-10-23
In this talk, I will introduce a class of independence relations which include free, Boolean and monotone independence in operator valued probability. I will briefly review some analytic properties of operator-valued free, Boolean and monotone convolutions. After that, I will show some analytic properties of two other important convolutions which are called orthogonal convolution and s-free convolution ( or say subordination convolution). We will see that most convolutions in our framework can be constructed from the orthogonal and the Boolean convolution whereas the s-free convolution is a powerful tool for studying the free additive convolution. Then I will show how to use matricial functions which are derived from Voiculescu's fully matricial function theory, to study relations between convolutions and transforms in operator-valued free probability. If time permits, I will simply explain how to compute large N laws of random matrices with entries of our new independent relations, and we will see that the large N laws are not always semicircular.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120169&date=2018-10-23Optimal robot action for and around people, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120052&date=2018-10-23
Estimation, planning, control, and learning are giving us robots that can generate good behavior given a specified objective and set of constraints. What I care about is how humans enter this behavior generation picture, and study two complementary challenges: 1) how to optimize behavior when the robot is not acting in isolation, but needs to coordinate or collaborate with people; and 2) what to optimize in order to get the behavior we want. My work has traditionally focused on the former, but more recently I have been casting the latter as a human-robot collaboration problem as well (where the human is the end-user, or even the robotics engineer building the system). Treating it as such has enabled us to use robot actions to gain information; to account for human pedagogic behavior; and to exchange information between the human and the robot via a plethora of communication channels, from external forces that the person physically applies to the robot, to comparison queries, to defining a proxy objective function.<br />
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The Berkeley Distinguished Lectures in Data Science, co-hosted by the Berkeley Institute for Data Science (BIDS) and the Berkeley Division of Data Sciences, features Berkeley faculty doing visionary research that illustrates the character of the ongoing data revolution. This lecture series is offered to engage our diverse campus community and enrich active connections among colleagues. All campus community members are welcome and encouraged to attend. Arrive at 3:30 PM for light refreshments and discussion prior to the formal presentation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120052&date=2018-10-23Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Oct 23
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120578&date=2018-10-23
Given a polynomial ring $C$ over a field and proper ideals $I$ and $J$ whose generating sets involve disjoint variables, we determine how to embed the associated primes of each power of $I+J$ into a collection of primes described in terms of the associated primes of select powers of $I$ and of $J$. We discuss applications to constructing primary decompositions for powers of $I+J$, and to attacking the persistence problem for associated primes of powers of an ideal. This is joint work with Irena Swanson found on arXiv:1806.03545.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120578&date=2018-10-23Topology Seminar (Introductory Talk), Oct 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120794&date=2018-10-24
The notion of geometrically finite discrete groups are originally defined by Ahlfors for subgroups of isometries of the 3-dimensional hyperbolic space, and alternative definitions of geometric finiteness were later given by Marden, Beardon and Maskit, and Thurston. We will focus on the definition given by Beardon and Marskit, and review Bishop’s characterization of geometrically finite discrete isometry subgroups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120794&date=2018-10-24Constructing (2+1)-dimensional KPZ evolutions, Oct 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120826&date=2018-10-24
The (d+1)-dimensional KPZ equation<br />
\[<br />
\partial_t h = \nu \Delta h + \frac{\lambda}{2}|\nabla h|^2 + \sqrt{D}\dot{W},<br />
\]<br />
in which \dot{W} is a space--time white noise, is a natural model for the growth of d-dimensional random surfaces. These surfaces are extremely rough due to the white noise forcing, which leads to difficulties in interpreting the nonlinear term in the equation. In particular, it is necessary to renormalize the mollified equations to achieve a limit as the mollification is turned off. The d = 1 case has been understood very deeply in recent years, and progress has been made in d ≥ 3, but little is known in d = 2. I will describe recent joint work with Sourav Chatterjee showing the tightness of a family of Cole--Hopf solutions to (2+1)-dimensional mollified and renormalized KPZ equations. This implies the existence of subsequential limits, which we furthermore can show do not coincide with solutions to the linearized equation, despite the fact that our renormalization scheme involves a logarithmic attenuation of the nonlinearity as the mollification scale is taken to zero.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120826&date=2018-10-24Topology Seminar (Main Talk), Oct 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120795&date=2018-10-24
In this talk, we focus on negatively pinched Hadamard manifolds which are complete, simply connected Riemannian manifolds with sectional curvature ranging between two negative constants. We use the techniques in geometric groups theory to generalize Bishop’s characterization of geometric finiteness to discrete isometry subgroups of negatively pinched Hadamard manifolds.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120795&date=2018-10-24Safe Learning in Robotics, Oct 24
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120922&date=2018-10-24
A great deal of research in recent years has focused on robot learning. In many applications, guarantees that specifications are satisfied throughout the learning process are paramount. For the safety specification, we present a controller synthesis technique based on the computation of reachable sets, using optimal control and game theory. In the first part of the talk, we will review these methods and their application to collision avoidance and avionics design in air traffic management systems, and networks of unmanned aerial vehicles. In the second part, we will present a toolbox of methods combining reachability with data-driven techniques inspired by machine learning, to enable performance improvement while maintaining safety. We will illustrate these “safe learning” methods on a quadrotor UAV experimental platform which we have at Berkeley, including demonstrations of motion planning around people.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120922&date=2018-10-24Paris/Berkeley/Bonn/Zürich Analysis Seminar, Oct 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120821&date=2018-10-25
Free boundary problems are those described by PDE's that exhibit a priori unknown (free) interfaces or boundaries. The Stefan problem is the most classical and motivating example in the study of free boundary problems. It describes the evolution of a medium undergoing a phase transition, such as ice passing to water. A milestone in this context is the classical work of Caffarelli (Acta Math. 1977), in which he established for the first time the regularity of free boundaries in the Stefan problem, outside a certain set of singular points. The goal of this talk is to present some new results concerning the size of the singular set in the Stefan problem, proving in particular that, in $\mathbb R^3$, for almost every time the free boundary is smooth, with no singularities. This is a joint work with A. Figalli and J. Serra.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120821&date=2018-10-25Applied Math Seminar, Oct 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120676&date=2018-10-25
A critical challenge in many modern scientific disciplines is deriving governing equations and forecasting models from data where derivation from first principals is intractable. The problem of learning dynamics from data is complicated when data is corrupted by noise, when only partial or indirect knowledge of the state is available, when dynamics exhibit parametric dependencies, or when only small volumes of data are available. In this talk I will discuss several methods for constructing models of dynamical systems from data including sparse identification for ordinary differential equations, sparse identification for partial differential equations with or without parametric dependencies, and approximation of dynamical systems governing equations using neural networks. Limitations of each approach and future research directions will be discussed.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120676&date=2018-10-25Berkeley Writers at Work, Oct 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119337&date=2018-10-25
Edward Frenkel, Professor of Mathematics, will be the featured writer in the Fall 2018 Berkeley Writers at Work series. The event will take place on Thursday, October 25, from noon to 1:30 pm in the Morrison Library, 101 Main Library, on the UC Berkeley campus.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=119337&date=2018-10-25Mathematics Department Colloquium, Oct 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120265&date=2018-10-25
Khovanov and Rozansky introduced a link homology theory which categorifies the HOMFLY polynomial. This invariant has a lot of interesting properties, but it is notoriously hard to compute. I will discuss recent progress in understanding HOMFLY homology and its surprising relation to algebraic geometry of the Hilbert scheme of points on the plane. The talk is based on joint works with Matt Hogancamp, Andrei Negut and Jacob Rasmussen.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120265&date=2018-10-25Combinatorics Seminar, Oct 29
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120979&date=2018-10-29
Macdonald introduced symmetric functions in two parameters that simultaneously generalize Hall—Littlewood symmetric functions and Jack symmetric functions. Opdam and Macdonald independently introduced nonsymmetric polynomial versions of these that Cherednik then generalized to any root system. Sanderson and Ion showed that these nonsymmetric Macdonald polynomials with one parameter specialized to 0 arise as characters for affine Demazure modules. Recently, I used the Haglund—Haiman—Loehr combinatorial formula for nonsymmetric Macdonald polynomials in type A to show that, in fact, the specialized nonsymmetric Macdonald polynomials are graded sums of finite Demazure characters in type A. In this talk, I’ll present joint work with Nicolle Gonzalez where we construct an explicit Demazure crystal for specialized nonsymmetric Macdonald polynomials, giving rise to an explicit formula for the Demazure expansion in terms of certain lowest weight elements. Connecting back with the symmetric case, this gives a refinement of the Schur expansion of Hall—Littlewood symmetric functions. <br />
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This talk assumes no prior knowledge of Macdonald polynomials, Demazure characters, or crystals.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120979&date=2018-10-29Probabilistic Operator Algebra Seminar, Oct 30
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120822&date=2018-10-30
I will present my recent results on operators on $L^p$ and $l^p$. These include (1) a characterization of the weak closure of ultrapowers of operators on $L^p$ and (2) $l^p$ versions of some results in the Brown-Douglas-Fillmore theory. Some applications will be shown: (1) ultrapowers of operators on $L^p$ have exactly 4 nontrivial invariant subspaces if the ultrafilter is selective (2) every unital homomorphism from C(M) into the Calkin algebra of $l^p$ can be expressed as a compression of a unital homomorphism from $C(M)$ into $B(l^p)$. Proofs of certain results are sketched. Some of the proofs are based on the proofs for Hilbert space and a probabilistic construction. However, the proof of homotopy invariance of the $Ext^-1$ group for $l^p$ uses an approach different from Kasparov's KK-theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120822&date=2018-10-30Rigidity and tolerance for perturbed lattices, Oct 31
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120793&date=2018-10-31
Consider a perturbed lattice {v+Y_v} obtained by adding IID d-dimensional Gaussian variables {Y_v} to the lattice points in Z^d. <br />
Suppose that one point, say Y_0, is removed from this perturbed lattice; is it possible for an observer, who sees just the remaining points, to detect that a point is missing?<br />
In one and two dimensions, the answer is positive: the two point processes (before and after Y_0 is removed) can be distinguished using smooth statistics, analogously to work of Sodin and Tsirelson (2004) on zeros of Gaussian analytic functions. (cf. Holroyd and Soo (2011) ). The situation in higher dimensions is more delicate; our solution depends on a game-theoretic idea, in one direction, and on the unpredictable paths constructed by Benjamini, Pemantle and the speaker (1998), in the other. (Joint work with Allan Sly).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120793&date=2018-10-31Topology Seminar (Main Talk), Oct 31
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120978&date=2018-10-31
This is joint work with Michael Lipnowski. We exhibit the first examples of hyperbolic three-manifolds for which the Seiberg-Witten equations do not admit any irreducible solution. Our approach relies on hyperbolic geometry in an essential way; it combines an explicit upper bound for the first eigenvalue on coexact 1-forms \(\lambda∗\) on rational homology spheres which admit irreducible solutions together with a version of the Selberg trace formula relating the spectrum of the Laplacian on coexact 1-forms with the volume and complex length spectrum of a hyperbolic three-manifold. Using these relationships, we also provide precise numerical bounds on \(\lambda∗\) for several hyperbolic rational homology spheres.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120978&date=2018-10-31