Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsStudent Probability/PDE Seminar, Feb 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123242&date=2019-02-01
Rezakhanlou has shown that the hydrodynamic behaviour of ASEP and other attractive asymmetric particle processes on $R^d$ is governed by a class of conservation laws. That is, macroscopic particle density profiles are given by entropy solutions of these conservation laws. In this talk, we will discuss Bahadoran’s recent extension of these results to bounded domains with particle reservoirs at the boundaries, and, if time permits, implications for hydrostatics and phase transitions. No prior knowledge of particle systems or conversation laws is necessary.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123242&date=2019-02-01Student Arithmetic Geometry Seminar, Feb 1
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123493&date=2019-02-01
In 2008, Bjorn Poonen announced the construction of a variety without rational points but no étale-Brauer obstruction to the existence of rational points. We attempt to create a new obstruction that explains Poonen s example by applying the étale-Brauer obstruction to a Zariski open cover of a variety. On the one hand, we prove a general result stating that this new obstruction explains every variety without rational points, over quadratic imaginary and totally real number fields. On the other hand, this method is not effective, as the set of adelic points of a non-proper variety is non-compact. Nonetheless, we show how this new obstruction can be applied in Poonen s example. In doing so, we analyze the example from an algebro-topological perspective via the étale homotopy obstruction of Harpaz-Schlank and prove some results of independent interest in this direction.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123493&date=2019-02-01Combinatorics Seminar, Feb 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122944&date=2019-02-04
We discuss recent developments in combinatorial algebraic geometry that were motivated by the study of rough paths in stochastic analysis. Every path in a real vector space is encoded in a signature tensor whose entries are iterated integrals. As the path varies over a nice family, we obtain an algebraic variety with interesting properties. Combinatorialists will especially enjoy the role played by Lyndon words and free Lie algebras.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122944&date=2019-02-04String-Math Seminar, Feb 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123316&date=2019-02-04
I will present the rank \(N\) magnificent four theory, which is the supersymmetric localization of \(U(N)\) super-Yang-Mills theory with matter on a Calabi-Yau fourfold, and conjecture an explicit formula for the partition function \(Z\): it has a free-field representation, and surprisingly it depends on Coulomb and mass parameters in a simple way. Based on joint work with N.Nekrasov.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123316&date=2019-02-04Probabilistic Operator Algebra Seminar, Feb 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123317&date=2019-02-04
In non-commutative probability the notion of stochastic independence is not unique. Therefore an extension of free probability which produces a larger variety of limit laws is certainly of interest. In this seminar we will review the notion of conditional freeness, introduced by Bozejko and Speicher. We will survey some of the combinatorial and analytic tools that are used in this setting and obtain the corresponding limit theorems. For example, a central limit theorem will be deduced, with instances of the limiting distributions including the arcsine, semicircle and Bernoulli distributions and certain deformations of these.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123317&date=2019-02-04Northern California Symplectic Geometry Seminar, Feb 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123490&date=2019-02-04
In this talk, I will discuss our understanding of contact submanifolds in higher dimensions. First, I will introduce the problems we are interested in and the current techniques we have to address them. In the main focus of the talk, I will present the construction of contactomorphic (and smoothly isotopic) contact submanifolds which are actually not contact isotopic. This resolves one of the main questions we had in higher dimensions. Finally, I will be introducing related works in progress and lines of future development. This talk is partially based on my work with J. Etnyre.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123490&date=2019-02-04Differential Geometry Seminar, Feb 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122887&date=2019-02-04
Cone spherical metrics are conformal metrics with constant curvature one with finitely many conical singularities on compact Riemann surfaces. The existence problem of such metrics has been open over twenty years. I will introduce the respectful audience some progress on this problem joint with Qing Chen, Xuemiao Chen, Yiran Cheng, Bo Li, Lingguang Li, Santai Qu, Jijian Song, Yingyi Wu and Xuwen Zhu.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122887&date=2019-02-04Statistical inference for infectious disease modeling, Feb 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123087&date=2019-02-04
We discuss two recent results concerning disease modeling on networks. The infection is assumed to spread via contagion (e.g., transmission over the edges of an underlying network). In the first scenario, we observe the infection status of individuals at a particular time instance and the goal is to identify a confidence set of nodes that contain the source of the infection with high probability. We show that when the underlying graph is a tree with certain regularity properties and the structure of the graph is known, confidence sets may be constructed with cardinality independent of the size of the infection set. In the scenario, the goal is to infer the network structure of the underlying graph based on knowledge of the infected individuals. We develop a hypothesis test based on permutation testing, and describe a sufficient condition for the validity of the hypothesis test based on automorphism groups of the graphs involved in the hypothesis test.<br />
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This is joint work with Justin Khim (UPenn).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123087&date=2019-02-04Northern California Symplectic Geometry Seminar, Feb 4
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123491&date=2019-02-04
The aim of this talk is to present a first attempt towards homotopy classification of holomorphic contact structures on Stein manifolds. We introduce the notion of a formal complex contact structure and show that any such structure on an odd dimensional Stein manifold $X$ is homotopic (through formal contact structures) to a genuine holomorphic contact structure on a Stein domain in X which is diffeotopic to $X$. The parametric h-principle also holds in this setting. On Stein threefolds we have a complete homotopy classification of formal complex contact structures. It is currently not understood whether these holomorphic contact structures could be realized on the whole Stein manifold $X$.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123491&date=2019-02-04Seminar 217, Risk Management: Endogenous risk, indirect contagion and systemic risk, Feb 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122086&date=2019-02-05
Deleveraging by financial institutions in response to losses may lead to contagion of losses across institutions with common asset holdings. Unlike direct contagion via counterparty exposures, this channel of contagion -which we call indirect contagion- is mediated through market prices and does not require bilateral exposures or relations. We show nevertheless that indirect contagion in the financial system may be modeled as a contagion process on an auxiliary network defined in terms of 'liquidity weighted portfolio overlaps' and we study various properties of this network using data from EU banks. Exposure to price-mediated contagion leads to the concept of indirect exposure to an asset class, as a consequence of which the risk exposure of a portfolio strongly depends on the asset holdings of large institutions in the network. We propose a systemic stress testing methodology for evaluating this risk exposure and construct a simple indicator of bank-level exposure to indirect contagion – the Indirect Contagion Index – based on the analysis of liquidity-weighted overlaps across bank portfolios. This indicator is shown to be strongly correlated with bank losses due to deleveraging and may be used to quantify the contribution of a financial institution to price-mediated contagion. <br />
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Joint work with Eric Schaanning (European Systemic Risk Board).<br />
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References:<br />
[1] Rama Cont, Eric F Schaanning (2016) Fire Sales, Indirect Contagion and Systemic Stress Testing. https://ssrn.com/abstract=2541114<br />
[2] Rama Cont, Eric F Schaanning (2017) Monitoring Indirect Contagion. https://ssrn.com/abstract=3195174http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122086&date=2019-02-053-Manifold Seminar, Feb 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123594&date=2019-02-05
A cube complex is a cell complex in which each n-cell is a n-dimensional cube. We'll define "special" cube complexes and explain their relationship to right-angled Artin groups. We'll also discuss some results about separability in their fundamental groups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123594&date=2019-02-053-Manifold Seminar, Feb 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123595&date=2019-02-05
A cube complex is a cell complex in which each n-cell is a n-dimensional cube. We'll define "special" cube complexes and explain their relationship to right-angled Artin groups. We'll also discuss some results about separability in their fundamental groups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123595&date=2019-02-05Representation Theory and Mathematical Physics Seminar, Feb 5
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123315&date=2019-02-05
We define the action of infinitely generated Temperley-Lieb algebra on the category of representations of the supergroup \(P(n)\). The supergroup in question is an interesting super analogue of the orthogonal and symplectic groups. As an application of this construction we get algorithm computing characters of irreducible representation of \(P(n)\) and some other esults. As n tends to infinity, we obtain a new universal tensor category equipped with Temperley-Lieb algebra action. In this way we obtain representation of TL in the Fock space.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123315&date=2019-02-05Harmonic Analysis Seminar, Feb 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123518&date=2019-02-06
Introduction to the work of L. Guth on application of the method of polynomial partitioning to Fourier restriction inequalities. This will be the first of a series of seminar meetings devoted to the 2016 article of Guth on this topic. Key concepts will be introduced. The method will be illustrated through an application to a simpler problem.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123518&date=2019-02-06Topology Seminar (Introductory Talk), Feb 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123519&date=2019-02-06
We'll review the definition of Ozsvath-Szabo's Heegaard Floer homology, and then define the involutive version constructed by Hendricks and Manolescu.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123519&date=2019-02-06A phase transition in a spatial permutation model on infinite trees, Feb 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123432&date=2019-02-06
Abstract: Spatial random permutation models are of physical interest due to connections to representations of certain gases such as helium as well as of the quantum Heisenberg ferromagnet. Physical phase transitions in these contexts correspond to the appearance of macro or infinite cycles in the permutation model. We study a spatial random permutation model on infinite trees with a time parameter T, a special case of which is the random stirring or random interchange process. The model on trees was first analysed by Björnberg and Ueltschi, who established the existence of infinite cycles for T slightly above a putatively identified critical value but left open behaviour at arbitrarily high values of T. We show the existence of infinite cycles for all T greater than a constant, thus classifying behaviour for all values of T and establishing the existence of a sharp phase transition. Our argument analyses a variant of simple random walk on the tree which is closely related.<br />
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Work with Alan Hammondhttp://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123432&date=2019-02-06Number Theory Seminar, Feb 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123596&date=2019-02-06
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123596&date=2019-02-06Thematic Seminar, Feb 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123593&date=2019-02-06
Let Mg be the moduli space of smooth curves of genus g. The tautological ring is a subring of the cohomology of Mg that was introduced by Mumford in the 1980s in analogy with the cohomology of Grassmannians. Work of Faber and Faber-Zagier in the 1990s led to two competing conjectural descriptions of the structure of the tautological ring. After reviewing these conjectures, I will discuss some of the evidence in recent years favoring one conjecture over the other.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123593&date=2019-02-06Center for Computational Biology Seminar, Feb 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120946&date=2019-02-06
Genomics, genetic rescue, and the future of conservation<br />
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Abstract: New technologies, including complete genome sequencing and genome engineering, promise to revolutionize conservation and slow the pace of the ongoing extinction crisis. However, the value of these technologies to conservation remains unclear. Using mountain lions from across their range and wolves from Isle Royale as examples, I will explore the value of complete genome reconstruction and analysis to conservation and management, focusing on what complete genomes can reveal that traditional genetic approaches cannot. I will also discuss the potential of genomics to inform genetic rescue interventions, and highlight some of the technical, ethical, and environmental hurdles that these particularly controversial technologies still face.<br />
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Bio: Beth Shapiro is an evolutionary biologist who specializes in the genetics of ice age animals and plants. As Professor of Ecology and Evolutionary Biology at UC Santa Cruz and HHMI Investigator, Beth uses DNA recovered from bones and other remains to study how species evolved through time and how human activities have affected and continue to affect this dynamic process. Her work focuses on organisms ranging from influenza to mammoths, asking questions about domestication, admixture, speciation, and pathogen evolution. Her current work develops techniques to recover increasingly trace amounts of DNA such as from environmental and forensic samples.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=120946&date=2019-02-06Topology Seminar (Main Talk), Feb 6
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123149&date=2019-02-06
We explain a generalization of the techniques that Hom introduced to construct an infinite-rank summand of the topologically slice knot concordance group. We generalize Hom's epsilon-invariant to the involutive Heegaard Floer homology constructed by Hendricks-Manolescu. As an application, we see that there is an infinite-rank summand of the homology cobordism group. This is joint work with Irving Dai, Jen Hom, and Linh Truong.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123149&date=2019-02-06Applied Math Seminar, Feb 7
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122772&date=2019-02-07
In this talk we discuss how to compute derivatives of long-time-averaged objectives with respect to multiple system parameters in chaotic systems, via the recently developed non-intrusive least-squares adjoint shadowing (NILSAS) algorithm.<br />
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First we review how to compute such derivatives via comparing the base trajectory and a shadowing trajectory, which is a new trajectory with perturbed parameter and perturbed initial condition, yet always lies close to the base trajectory. Then we review how to compute such shadowing trajectory via a `non-intrusive' minimization problem on the unstable subspace. Then we show our recent work on defining and proving the unique existence of adjoint shadowing directions. Then we develop the NILSAS algorithm, whose cost is independent of number of parameters, and its implementation requires only minor modifications to existing adjoint solvers. Finally, we show an application, by Chaitanya Talnikar, of NILSAS on a weakly turbulent flow over a three-dimensional cylinder at Re=1100, where the cost of NILSAS is similar to simulating the flow problem.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122772&date=2019-02-07Special Seminar, Feb 7
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123676&date=2019-02-07
Tschinkel will discuss effectivity issues in several problems in arithmetic geometry, the study of solutions of systems of polynomial equations with integral coefficients.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123676&date=2019-02-07Inverse RNA folding and Computational Riboswitch Detection, Feb 7
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123217&date=2019-02-07
The inverse RNA folding problem for designing sequences that fold into a given RNA secondary structure was introduced in the early 1990's in Vienna. Using a coarse-grain tree graph representation of the RNA secondary structure, we extended the inverse RNA folding problem to include constraints such as thermodynamic stability and mutational robustness, developing a program called RNAexinv. In the next step, we formulated a fragment-based design approach of RNA sequences that can be useful to practitioners in a variety of biological applications. In this shape-based design approach, specific RNA structural motifs with known biological functions are strictly enforced while others can possess more flexibility in their structure in favor of preserving physical attributes and additional constraints. Our program is called RNAfbinv (recently extended to incaRNAfbinv by incorporating a weighted sampling approach borrowed from incaRNAtion).<br />
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Detection of riboswitches in genomic sequences using structure based methods, including the use of incaRNAfbinv, will also be discussed.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123217&date=2019-02-07Mathematics Department Colloquium, Feb 7
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123590&date=2019-02-07
A conjecture of Kontsevich says that the Fukaya category of a symplectic manifold having an additional volume form, should have a stability condition where the stable objects are represented by possibly singular "special Lagrangians". This statement has a nice expression, in the case where we look at the Fukaya-Seidel category of a Riemann surface with coefficients in a fiber category. The special Lagrangians are identified with the spectral networks of Gaiotto-Moore-Neitzke. In joint work with Haiden, Katzarkov and Pandit, in progress, we treat a first rather simple case but one that leads already to some interesting pictures.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123590&date=2019-02-07GRASP seminar, Feb 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123723&date=2019-02-08
Given a real polynomial $p$ in $n$-variables, we define a family of distributions over $\{\lambda \in \mathbb C | \text {Re}\lambda >0\}$, generalizing the Γ-function. We claim that it is possible to analytically continue this family, exactly the same way as is traditionally done for the Γ-function, using the existence of the so-called Bernstein-Sato polynomial, $b_p$, of $p$.<br />
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We compute some of examples of these polynomials, then show that their existence is equivalent to a purely module-theoretical question. This takes us into the theory of holonomic $\mathcal D$-modules on $\mathbb A^n$, which we shall use as a diving board into the theory of $\mathcal D$-modules and to solve the original analytic question.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123723&date=2019-02-08A planet-scale playground for data scientists - Google Maps, Feb 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123494&date=2019-02-08
Are there good soba noodle places nearby? How do I get to JFK by train? When does this park close? Show me Stonehenge! Helping people explore and get things done in the real world is the task our team has taken on, and it is a rather challenging one. In this talk I will describe the technical complexity of creating models that reflect the real world for tools such as Google Maps, Search and Google Earth.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123494&date=2019-02-08Logic Colloquium, Feb 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123314&date=2019-02-08
I will present a few basic applications of model theory in theoretical computer science, e.g. in verification, databases, and algorithms. I will also briefly discuss some links between notions from graph theory and stability theory.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123314&date=2019-02-08Student 3-Manifold Seminar, Feb 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123675&date=2019-02-08
Simplified, the loop theorem states that if the induced map $\pi _1(\partial M)\to \pi _1(M)$ for a $3$-manifold $M$ is not injective, then there is a nullhomotopy of an essential loop in $\partial M$ that can be represented by an embedded disk. We will go through the proof of Stalling's formulation of the loop theorem using Papakyriakopoulos's tower construction and discuss some applications.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123675&date=2019-02-08Student Arithmetic Geometry Seminar, Feb 8
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123722&date=2019-02-08
Last week, I explained the (etale) Brauer-Manin obstruction and Poonen's counterexample. I also stated my result that the Brauer-Manin obstruction on Zariski open covers is enough to (theoretically) determine the existence of rational points. This week, I will say more about how to prove this result. I will also explain the idea behind the etale homotopy obstruction to the local-global principle and how it sheds new light on the more classical obstructions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123722&date=2019-02-08Combinatorics Seminar, Feb 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122943&date=2019-02-11
In an n-team tournament, each pair of teams plays a win-lose match. Landau's Theorem (1953) states that a sequence (x1,x2,...,xn), written in non-decreasing order, is the score sequence of some n-team tournament if and only if it is majorized by (0,1,...,n-1), meaning that all partial sums x1+...+xk are at least k(k-1)/2, with equality for k=n. Moon's Theorem (1963) extends this to random tournaments, in which case x is the mean score sequence. We give two short, probabilistic proofs of Moon's Theorem, one of which is fully constructive. We also show that the set of mean score sequences is the closure of those arising from the Bradley-Terry model (a model for sports results), where for a sequence of abilities (a1,a2,...,an), the probability that team i beats j is L(ai-aj), where $L(x)=e^x/(1+e^x)$ is the logistic function. This talk offers a glimpse into a longstanding mystery: the lack of a canonical construction for a joint distribution in the representation theorem (Strassen 1965) for convex order. This is joint work with David Aldous.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122943&date=2019-02-11Probabilistic Operator Algebra Seminar, Feb 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122178&date=2019-02-11
It is known that the property of being free (or asymptotically free) for Haar unitaries remains to some extent, when the unitaries are tensored with other unitaries. In the recent years, we investigated the question of, to which extent this property holds. For example, does it hold when tensored by non-unitary operators ? When does asymptotic freeness hold strongly (in norm) ? In traffics ? etc. We have complete answers to some questions, and partial answers to others. I will review what is known at this point. This talk is based on various papers in collaboration with people including Charles Bordenave (CNRS), Camille Male (CNRS), and Pierre Ives Gaudreau Lamarre (Princeton).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122178&date=2019-02-11Daniel Lacker - Beyond Mean Field Limits: Local Dynamics For Large Sparse Networks Of Interacting Diffusions, Feb 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123363&date=2019-02-11
Abstract: We study large systems of stochastic processes (particles) in which each particle is associated with a vertex in a graph and interacts only with its neighbors. When the graph is complete and the numbers of particles grows to infinity, the system is well-described by a McKean-Vlasov equation, which describes the behavior of one typical particle. For general (sparse) graphs, the system is no longer exchangeable, and the mean field approximation is not valid. Nevertheless, if the underlying graph is locally tree-like, we show that a single particle and its nearest neighbors are characterized by a peculiar but autonomous set of "local dynamics." This work is motivated in part by recent mean field models of inter-bank lending, which capture several dynamic features of systemic risk but thus far lack realistic network structure. Joint work with Kavita Ramanan and Ruoyu Wu.<br />
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Bio: Daniel Lacker is an assistant professor in Industrial Engineering and Operations Research (IEOR) at Columbia University. From 2015-2017 he was an NSF postdoctoral fellow in Applied Mathematics at Brown University, and before that he completed his Ph.D. in 2015 at Princeton University in the department of Operations Research and Financial Engineering (ORFE). So far his research has focused largely on the theory and applications of mean field games, where the areas of interacting particle systems, stochastic control, and game theory intersect. More broadly, he is interested in many topics in probability and mathematical finance.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123363&date=2019-02-11String-Math Seminar, Feb 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123492&date=2019-02-11
A classical result of Turaev identifies the skein algebra of the annulus with the algebra of symmetric functions in infinitely many variables. Queffelec and Roze categorified this using annular webs and foams. I will recall their construction and compute explicit symmetric functions and their categorical analogues for some links. As an application, I will describe spectral sequences computing categorical invariants of generalized Hopf links. The talk is based on a joint work with Paul Wedrich.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123492&date=2019-02-11Arithmetic Geometry and Number Theory RTG Seminar, Feb 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123517&date=2019-02-11
The topology of an algebraic variety is a central subject in algebraic geometry. Instead of a variety, we consider the topology of a pair (X,D) which is a variety X with a divisor D, but in the coarsest level. More precisely, we study the dual complex defined as the combinatorial datum characterizing how the components of D intersect with each other. We will discuss how to use the minimal model program (MMP) to investigate it. We will also discuss some applications, including in the construction of non-archimedean SYZ fibrations.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123517&date=2019-02-11Chiwei Yan - Transportation Optimization: Data-enabled Advances in a Sharing Economy, Feb 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122323&date=2019-02-11
Abstract: The transportation and logistics industries are undergoing a round of revolutionary innovation. This innovation is fueled by two key drivers: (1) the growing availability of data, and (2) new operational paradigms in a sharing economy. This talk focuses on showcasing how new models, enabled by the prevalence of data, can lead to significant value in operational decision-making.<br />
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We begin by presenting our research that shows how trip data in bike-sharing systems can be mined to infer rider substitution behaviors when there are bike or dock shortages. Based on a non-parametric ranking-based choice model, we propose efficient enumeration procedures and first-order methods to solve the large-scale estimation problem by exploiting problem structure. We prove consistency results of our method. We then demonstrate, with Boston Hubway data, that ridership can be significantly improved through effective inventory allocation operations with better demand modeling.<br />
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Next, we describe a recent work in which we propose a new car-pooling mechanism in ride-hailing, called dynamic waiting which varies rider waiting before dispatch. The goal is to limit price volatility in ride-hailing services by reducing the role of surge pricing. We describe a steady-state model depicting the long-run average performance of a ride-hailing service, and characterize the system equilibrium. Calibrating the model using Uber data, we reveal insights on welfare-maximizing pricing and waiting strategies. We show that, with dynamic waiting, price can be lowered, its variability is mitigated and total welfare is increased. <br />
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Bio: Chiwei Yan received his PhD from the Operations Research Center at MIT in 2017. His current research interest is in transportation and logistics, with a focus on data-driven optimization and emerging problems in a sharing economy. He is a recipient of the Best Dissertation Award Honorable Mention and the Outstanding Paper Award in Air Transportation from INFORMS Transportation Science and Logistics Society, the Best Dissertation Award from INFORMS Aviation Application Section, the AGIFORS Anna Valicek Award, and the UPS Doctoral Fellowship, among others. His research involves collaborations with both the private and public sectors, including the Federal Aviation Administration, Sabre Airline Solutions, Boston Hubway Bikes and Uber. Before coming to MIT, he obtained the Bachelor of Science in Industrial Engineering from Tsinghua University.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122323&date=2019-02-11Analysis and PDE Seminar, Feb 11
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123592&date=2019-02-11
A control system is a dynamical system on which one can act thanks to what is called the control. For example, in a car, one can turn the steering wheel, press the accelerator pedal etc. These are the control(s). One of the main problems in control theory is the controllability problem. One starts from a given situation and there is a given target. The controllability problem is to see if, by using some suitable controls depending on time, one can move from the given situation to the desired target. We study this problem with a special emphasis on the case where the nonlinearities play a crucial role. We first recall some classical results on this problem for finite dimensional control systems. We explain why the main tool used for this problem in finite dimension, namely the iterated Lie brackets, is difficult to use for many important control systems modeled by partial differential equations. We present methods to avoid the use of these iterated Lie brackets. We give applications of these methods to various physical control systems (Euler and Navier-Stokes equations of incompressible fluids, shallow water equations, Korteweg-de Vries equations).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123592&date=2019-02-11Seminar 217, Risk Management: Computation of Optimal Conditional Expected Drawdown Portfolios, Feb 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122087&date=2019-02-12
We introduce two approaches to computing and minimizing the risk measure Conditional Expected Drawdown (CED) of Goldberg and Mahmoud (2016). One approach is based on a continuous-time formulation yielding a partial differential equation (PDE) solution to computing and minimizing CED while another is a sampling based approach utilizing a linear program (LP) for minimizing CED.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122087&date=2019-02-123-Manifold Seminar, Feb 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123754&date=2019-02-12
A knot or link $L$ in $S^3$ is called universal if every closed orientable $3$-manifold can be represented as a cover branched over $L$, with some examples including the Borromean rings, the figure-eight knot, and 2-bridge non-torus links. Some such $L$ are the singular locus of an orbifold ${\mathbb H}^3/\Gamma \cong S^3$ for Γ an arithmetic subgroup of the linear algebraic group of isometries of ${\mathbb H}^3$, which gives every closed orientable manifold the structure of an arithmetic orbifold. A natural question, then, is which hyperbolic orbifolds have an arithmetic orbifold group. We will discuss a paper of Hilden-Lozano-Montesinos showing that the orbifold from the $n$-fold cyclic branched cover of the figure-eight knot is arithmetic only at the values $n=4,5,6,8,12,\infty $.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123754&date=2019-02-12Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Feb 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123673&date=2019-02-12
I will explain the notion of terminal singularities. This is the mildest class of singularities that appears in constructing minimal models of algebraic varieties. In characteristic zero, terminal singularities are automatically Cohen-Macaulay, and this is very useful for the minimal model program. I will present the first known terminal singularity of dimension 3 which is not Cohen-Macaulay; it has characteristic 2. The example is surprisingly easy to describe. Many open problems remain, as I will discuss.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123673&date=2019-02-12Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Feb 12
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123674&date=2019-02-12
In this talk I will give a description of the following recent result: the non-Archimedean skeleton of the d-th symmetric power of a smooth projective algebraic curve X is naturally isomorphic to the d-th symmetric power of the tropical curve that arises as the non-Archimedean skeleton of X. In the talk I will give all necessary background definitions for understanding the above statement and I will sketch the proof.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123674&date=2019-02-12Harmonic Analysis Seminar, Feb 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123757&date=2019-02-13
Continuation of discussion of “A restriction estimate using polynomial partitioning” by L. Guth. The polynomial partitioning lemma. Construction of the wave packet decomposition and proof of its main properties. $L^2$ bounds for sums of wave packets.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123757&date=2019-02-13Topology Seminar (Introductory Talk), Feb 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123752&date=2019-02-13
I will give a very general overview of lattices in semisimple Lie groups, and a brief introduction to thin groups. This latter class of groups is a current "hot topic", with a plethora of applications to subjects as diverse as number theory, hyperbolic geometry, and quantum computation.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123752&date=2019-02-13Large Deviations of Random Projections of High-dimensional Measures, Feb 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123749&date=2019-02-13
Properties of random projections of high-dimensional probability measures are of interest in a variety of fields, including asymptotic convex geometry, and high-dimensional statistics and data analysis. A particular question of interest is to identify what properties of the high-dimensional measure are captured by its lower-dimensional projections. While fluctuations of these projections have been well studied over the past decade, we describe more recent work on both annealed and quenched large deviations principles and associated conditional limit theorems for multidimensional projections. This talk is based on joint works with <br />
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Nina Gantert, Steven Kim and Yin-Ting Liao.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123749&date=2019-02-13Number Theory Seminar, Feb 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123883&date=2019-02-13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123883&date=2019-02-13Topology Seminar (Main Talk), Feb 13
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123753&date=2019-02-13
A celebrated result of Margulis says that among irreducible lattices in higher rank semi-simple Lie groups, arithmetic lattices are characterized as those having dense commensurators. If the subgroup of the Lie group is Zariski dense and discrete but is no longer assumed to have finite covolume (that is, to be thin), then no such definitive dichotomy exists. A heuristic due to Y. Shalom says that thin subgroups should be thought of as non-arithmetic. In this talk I will discuss a theorem confirming Shalom's heuristic for certain naturally defined thin subgroups of \(PSL_2(Z)\). This is joint work with M. Mj.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123753&date=2019-02-13Integrated Analysis of Cancer Data: Multi-omic Clustering and Personalized Ranking of Driver Genes, Feb 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123218&date=2019-02-14
Large biological datasets are currently available, and their analysis has applications to basic science and medicine. While inquiry of each dataset separately often provides insights, integrative analysis may reveal more holistic, systems-level findings. We demonstrate the power of integrated analysis in cancer on two levels: (1) in analysis of one omic in many cancer types together, and (2) in analysis of multiple omics for the same cancer. In both levels we develop novel methods and observe a clear advantage to integration. We also describe a novel method for identifying and ranking driver genes in an individual's tumor and demonstrate its advantage over prior art.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123218&date=2019-02-14Center for Computational Biology and Koret Berkeley Tel Aviv Initiative Seminar, Feb 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123547&date=2019-02-14
Integrated analysis of cancer data: multi-omic clustering and personalized ranking of driver genes<br />
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Abstract: Large biological datasets are currently available, and their analysis has applications to basic science and medicine. While inquiry of each dataset separately often provides insights, integrative analysis may reveal more holistic, systems-level findings. We demonstrate the power of integrated analysis in cancer on two levels: (1) in analysis of one omic in many cancer types together, and (2) in analysis of multiple omics for the same cancer. In both levels we develop novel methods and observe a clear advantage to integration. We also describe a novel method for identifying and ranking driver genes in an individual's tumor and demonstrate its advantage over prior art.<br />
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Biography: Ron Shamir received his PhD from UC Berkeley. He is a Sackler professor of Bioinformatics in the Blavatnik School of Computer Science at Tel Aviv University (TAU). His group develops algorithms in bioinformatics for understanding the genome and human disease. Software tools developed by Shamir’s group are in use around the world. Shamir is the founder and head of the Edmond J. Safra Center for Bioinformatics at TAU. He has published about 300 scientific works, including 17 books and edited volumes, and has supervised more than 50 research students. He was on the founding steering committee of RECOMB, co-founded the Israeli Society of Bioinformatics and Computational Biology, and was society president. He is a recipient of the Landau Prize in Bioinformatics, the Kadar family prize for excellence in research, and a Fellow of the ISCB and the ACM.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123547&date=2019-02-14Mathematics Department Colloquium, Feb 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123591&date=2019-02-14
Consider an algebraic curve in 3-space; when projected generically to a plane, it will acquire a number of double points. This number depends only on the degree and the genus of the curve. Computing similar numbers when the curve is replaced by a surface arbitrarily embedded will be the subject of the lecture. One key difference with the curve case is the fact that we have to work with the Hilbert scheme of k points, instead of the k-th symmetric product, and I will spend some time on the construction of the Hilbert scheme. The main result I will present is the Lehn conjecture, now a theorem, computing all these numbers for all surfaces in terms of their numerical (complex cobordism) invariants.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123591&date=2019-02-14Student Probability/PDE Seminar, Feb 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123869&date=2019-02-15
In this presentation, a classic model known as "small random perturbation of dynamical systems" studied by Freidlin and Wentzell in 1960s is revisited. Freidlin and Wentzell deduced a large-deviation principle for this model, and this result was considerably refined in 2004 by Bovier et. al. In this presentation, we discuss a further refinement of this result via a new technology based on the analysis of suitable Poisson equations. This talk is based on the joint work with F. Rezakhanlou and C. Landim.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123869&date=2019-02-15Beste Basciftci - Value of Optimization under Uncertainty and Integration of Data in Energy Supply Chains, Feb 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122433&date=2019-02-15
Abstract: Most of the real-life problems involve uncertainty, which need to be delicately integrated into the decision-making processes. In this talk, we present various stochastic optimization techniques motivated by maintenance, operations and capacity expansion planning problems in energy systems. In the first part of the talk, our aim is to effectively model and solve the integrated condition-based maintenance and operations scheduling problem of a fleet of generators. We develop a data-driven optimization framework that explicitly considers the effect of the sensor-driven generator failure scenarios and operations schedules on the generators’ degradation levels to construct a reliable and cost-efficient plan. In the second part of the talk, we shift our focus to a more generic problem setting in sequential decision-making under uncertainty. Although two-stage and multi-stage stochastic programming are among the key methodologies to address multi-period problems under uncertainty, they might not provide adequate solutions under limited flexibility by resulting in either fully static or dynamic policies. We propose a novel adaptive stochastic programming approach, in which we optimize the time to revise decisions. We provide theoretical bounds on the performance of the proposed approach compared to the static and dynamic approaches, and present practical implications of the choice of the revision time. We also tailor solution algorithms using our analytical analyses and derive their approximation guarantees. To illustrate our results, we study a generation expansion planning problem demonstrating the advantages of the adaptive approach over existing policies. <br />
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Bio: Beste Basciftci is currently a PhD candidate in Operations Research at the H. Milton Stewart School of Industrial and Systems Engineering, Georgia Institute of Technology, with a minor in Statistics. She received her bachelor's degrees in Industrial Engineering and Computer Engineering from Boğaziçi University with High Honors. She also hold a master's degree in Industrial Engineering from Boğaziçi University. She is broadly interested in data-driven decision making problems under uncertainty. Methodologically, her research focuses on developing mixed-integer, stochastic programming and distributionally robust optimization approaches to address operations research/management related problems, specifically for applications in energy, supply chains, production systems, and healthcare operations. Her research also involves developing and integrating statistical modeling and business analytics approaches to the subsequent decision-making processes.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122433&date=2019-02-15Student 3-Manifold Seminar, Feb 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123938&date=2019-02-15
A version of the Papakyriakopoulos Sphere Theorem states that a compact $3$-manifold with nontrivial $\pi _2$ has a two-sided embedded sphere or projective plane representing a nontrivial homotopy class. We will discuss ends of groups and how the theorem follows from Stallings's theorem on finitely generated groups with more than one end.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123938&date=2019-02-15Seminar 217, Risk Management: Sustainable Responsible Investing and the Cross-Section of Return and Risk, Feb 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122088&date=2019-02-19
The identification of factors that predict the cross-section of stock returns has been a focus of asset pricing theory for decades. We address this challenging problem for both equity performance and risk, the latter through the maximum drawdown measure. We test a variety of regression-based models used in the field of supervised learning including penalized linear regression, tree-based models, and neural networks. Using empirical data in the US market from January 1980 to June 2018, we find that a number of firm characteristics succeed in explaining the cross-sectional variation of active returns and maximum drawdown, and that the latter has substantially better predictability. Non-linear models materially add to the predictive power of linear models. Finally, environmental, social, and governance impact enhances predictive power for non-linear models when the number of variables is reduced.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122088&date=2019-02-19Representation Theory and Mathematical Physics Seminar, Feb 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123907&date=2019-02-19
We define the action of infinitely generated Temperley-Lieb algebra on the category of representations of the supergroup \(P(n)\). The supergroup in question is an interesting super analogue of the orthogonal and symplectic groups. As an application of this construction we get algorithm computing characters of irreducible representation of \(P(n)\) and some other esults. As n tends to infinity, we obtain a new universal tensor category equipped with Temperley-Lieb algebra action. In this way we obtain representation of TL in the Fock space.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123907&date=2019-02-19Bowen Lectures, Feb 19
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123692&date=2019-02-19
The symmetries of systems of polynomial equations can be be understood in terms of the geometry of the variety of zeroes (or solution set) of the polynomials. Roughly speaking, there are 3 kinds of geometries corresponding to positive, zero and negative curvature giving rise to 3 different kinds of symmetry groups. In this lecture, I will discuss recent advances in algebraic geometry that lead to very precise results on the structure of these symmetry groups.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123692&date=2019-02-19Topology Seminar (Introductory Talk), Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123354&date=2019-02-20
The Chekanov-Eliashberg algebra is a powerful Legendrian isotopy invariant that is defined by counts of pseudoholomorphic discs. We give an introduction to both analytical and algebraic aspects of the theory, perform calculations in both low and high dimension, and present some open problems.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123354&date=2019-02-20Algorithmic Pirogov-Sinai theory, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123922&date=2019-02-20
What is the connection between a phase transition in a statistical physics model and the computational complexity of sampling from the given model? In the setting of the hard-core and Potts models on lattices, it is known that in the phase coexistence regime the Glauber dynamics mix slowly. Using some of the same tools used to prove slow mixing (the cluster expansion and Pirogov-Sinai theory), we give efficient algorithms to approximate the partition function of and sample from the hard-core and Potts models at sufficiently low temperatures on the lattice. Our algorithms are inspired by Barvinok's approach to polynomial approximation. Joint work with Tyler Helmuth and Guus Regts.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123922&date=2019-02-20Statistics on Shape Data: Correcting an Asymptotic Bias in Template Shape Estimation, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123897&date=2019-02-20
Computational Anatomy aims to model and analyze healthy and pathological distributions of organ shapes. We are interested in the computational representation of the brain anatomy using brain MRIs (Magnetic Resonance Imaging). How can we define the notion of brain shapes and how can we learn their distribution in the population? Landmarks’ shapes, curve shapes or surface shapes can be seen as the remainder after we have filtered out the object position and orientation. As such, shape data belong to quotient spaces. We present “Geometric Statistics”, a framework for data belonging to non-Euclidean spaces like quotient spaces of Riemannian manifolds. We use tools of Geometric Statistics and Riemannian geometry to prove that the “template shape estimation” algorithm, used for more than 15 years in medical imaging (and signal processing), has an asymptotic bias. The geometric intuition provided by the study leads us to design new bias correction methods. We present experimental results on simulated and real data, including a first bias quantification of the brain template computed from MRIs.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123897&date=2019-02-20Bowen Lectures, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123693&date=2019-02-20
Algebraic varieties are geometric objects defined by polynomial equations. The minimal model program (MMP) is an ambitious program that aims to classify algebraic varieties. According to the MMP, there are 3 building blocks: Fano varieties, Calabi-Yau varieties and varieties of general type which are higher dimensional analogs of Riemann Surfaces of genus 0,1 or at least 2 respectively. In this talk I will recall the general features of the MMP and discuss recent advances in our understanding of Fano varieties and varieties of general type.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123693&date=2019-02-20Special Analysis Seminar, Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123970&date=2019-02-20
Physical experiments show that interfaces between dissimilar media act as stable channels for the propagation of energy. In discrete models, this stability is explained via an index-like theorem: the bulk edge correspondence. I will first review this principle, which connects the effective number of waves propagating along the interface (a spectral invariant) to a Chern number (a topological invariant).<br />
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I will then focus on a PDE modeling conduction in a graphene layer with a line defect. In a perturbative regime, Fefferman–Lee-Thorp–Weinstein–Zhu constructed waves propagating along the defect. I will show that precisely two of them are topologically stable: they persist outside the perturbative regime. I will then calculate the associated Chern number: it is 2 or -2. These results illustrate the bulk-edge correspondence in a continuous setting.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123970&date=2019-02-20Topology Seminar (Main Talk), Feb 20
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123319&date=2019-02-20
We use techniques from persistence homology applied to the Chekanov-Eliashberg algebra in order to obtain a restriction on the oscillatory norm of a contact Hamiltonian that displaces a Legendrian in the contact vector space from its image under the Reeb flow. These techniques are also used to show that a Legendrian which admits an augmentation cannot \(C^0\)-approximate a loose Legendrian, and to obstruct the existence of small positive Legendrian loops. This is joint work with M. Sullivan.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123319&date=2019-02-20Applied Math Seminar, Feb 21
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123967&date=2019-02-21
The Grassmann manifold Gr(m,n) is the set of n-dimensional subspaces in $\mathbb R^m$ (assuming m >n), and is used in many science and engineering applications. A point in Gr(m,n) can be represented by an orthogonal matrix of size m by n, multiplied by another arbitrary orthogonal matrix of size n by n. In quantum chemistry and in particular the widely used density functional theory (DFT), this arbitrary orthogonal matrix is referred to as the gauge. Physical quantities such as energies and electron densities should be independent of the gauge choice. In this talk, I am going to discuss the interplay between gauge-dependent and gauge-independent quantities in quantum chemistry along three recent directions: time-dependent density functional theory, electron localization, and self-consistent field iteration. In each case, the focus on the gauge-independent representation of the Grassmann manifold brings interesting, and sometimes surprising numerical benefits.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123967&date=2019-02-21Mathematics Department Colloquium/Bowen Lectures, Feb 21
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123694&date=2019-02-21
After recent spectacular progress in the classification of varieties over an algebraic closed field of characteristic 0 (e.g. the solution set of a system of polynomial equations defined by $p_1,...,p_r$ in $C[x_1,...,x_n]$) it is natural to try and understand the geometry of varieties defined over an algebraically closed field of characteristic $p >0$. Many technical difficulties arise in this context. Nevertheless, there has been much progress recently. In particular, the MMP was established for 3-folds in characteristic $p >5$ by work of Birkar, Hacon, Xu and others. In this talk, we will explain some of the challenges and the recent progress in this active area of research.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123694&date=2019-02-21Logic Colloquium, Feb 22
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123724&date=2019-02-22
The discovery of non euclidean geometry in the early nineteenth century had shaken the beliefs and conjectures of more than two thousand years and changed the picture we had for mathematics, physics and even philosophy. Lobachevsky and Bolyai independently around 1830 discovered hyperbolic geometry. A notable distinguish feature of hyperbolic geometry is its negative curvature in a way that the sum of angles of a triangle is less than π. Gromov much later in 1987 introduced hyperbolic groups which are groups acting "nicely" on hyperbolic spaces, or equivalently finitely generated groups whose Cayley graphs are "negatively curved". Main examples are free groups and almost all surface groups. The fascinating subject of hyperbolic groups touches on many mathematical disciplines such as geometric group theory, low dimensional topology and combinatorial group theory. It is connected to model theory through a question of Tarski.<br />
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Tarski asked around 1946 whether non abelian free groups have the same common first order theory. This question proved extremely hard to answer and only after more than fifty years in 2001 Sela and Kharlampovich-Myasnikov answered it positively. Both works are voluminous and have not been absorbed yet. The techniques almost exclusively come from the disciplines mentioned above, hence it is no wonder that the question had to wait for their development. The great novelty of the methods and the depth of the needed results have made it hard to streamline any of the proofs. Despite the difficulties there is some considerable progress in the understanding of the first order theory of "the free group" and consequently first order theories of hyperbolic groups from the scopes of basic model theory, Shela's classification theory and geometric stability. In this talk I will survey what is known about these theories and what are the main open questions.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123724&date=2019-02-22Combinatorics Seminar, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123672&date=2019-02-25
We provide a characterization of the crystal bases for the quantum queer superalgebra recently introduced by Grantcharov et al.. This characterization is a combination of local queer axioms generalizing Stembridge's local axioms for crystal bases for simply-laced root systems, which were recently introduced by Assaf and Oguz, with further axioms and a new graph $G$ characterizing the relations of the type $A$ components of the queer crystal. We provide a counterexample to Assaf's and Oguz' conjecture that the local queer axioms uniquely characterize the queer supercrystal. We obtain a combinatorial description of the graph $G$ on the type $A$ components by providing explicit combinatorial rules for the odd queer operators on certain highest weight elements.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123672&date=2019-02-25Probabilistic Operator Algebra Seminar, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122911&date=2019-02-25
Consider a quantum system consisting of N particles, and assume that it is in a random pure state (i.e., uniform over the sphere of the corresponding Hilbert space H). Let A and B be two subsystems consisting of k particles each. Then there exists a threshold value $k_0 \sim N/5$ such that<br />
<br />
(i) if $k > k_0$, then A and B typically share entanglement<br />
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(ii) if $k < k_0$, then A and B typically do not share entanglement.<br />
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We give precise statements of results of the above type and outline the arguments which involve random matrices, majorization, and various concepts/techniques from geometric functional analysis.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122911&date=2019-02-25String-Math Seminar, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123213&date=2019-02-25
Virasoro constraints are omnipresent in enumerative geometry. Recently, Kontsevich and Soibelman introduced a generalization of Virasoro constraints in the form of Airy structures. It can also be understood as an abstract framework underlying the topological recursion of Chekhov, Eynard and Orantin. In this talk I will explain how the triumvirate of Virasoro constraints, Airy structures and topological recursion can be generalized to W-algebra constraints, higher Airy structures and higher topological recursion. I will briefly discuss the enumerative geometric meaning of the resulting W-constraints in the context of open and closed intersection theory on the moduli spaces or curves with r-spin structure and its variants.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123213&date=2019-02-25Arithmetic Geometry and Number Theory RTG Seminar, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123755&date=2019-02-25
The Breuil-Mezard conjecture predicts the geometry of local Galois deformation rings with p-adic Hodge theory condition in terms of modular representation theory. I will begin by reformulating this conjecture in terms of the Emerton-Gee moduli stack of mod p Galois representations. I will then describe joint work in progress with Daniel Le, Bao V. Le Hung, and Stefano Morra where we prove the conjecture in generic situations for a class of potentially crystalline deformation rings. The key ingredient is the construction of a local model which models the singularities of these Galois deformation rings.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123755&date=2019-02-25Nonlinear Algebra Seminar, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123870&date=2019-02-25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123870&date=2019-02-25Differential Geometry Seminar, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123671&date=2019-02-25
We show that a Ricci flow in four dimensions can develop singularities modeled on the Eguchi-Hanson space. In particular, we prove that starting from a class of asymptotically cylindrical $U(2)$-invariant initial metrics on $TS^2$, a Type II singularity modeled on the Eguchi-Hanson space develops in finite time. Furthermore we show that in our setup blow-up limits at larger scales are isometric to either (i) the flat $\mathbb R^4 /\mathbb Z_2$ orbifold, (ii) a rotationally symmetric, positively curved, asymptotically cylindrical ancient orbifold Ricci flow on $\mathbb R^4/\mathbb Z_2$, or (iii) the shrinking soliton on $\mathbb R \times \mathbb R P^3$. As a byproduct of our work, we also prove the existence of a new family of Type II singularities caused by the collapse of a two-sphere of self-intersection $|k| \geq 3$.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123671&date=2019-02-25Nonlinear Algebra Seminar, Feb 25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123871&date=2019-02-25
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123871&date=2019-02-25Seminar 217, Risk Management: Collateralized Networks, Feb 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122089&date=2019-02-26
We study the spread of losses and defaults through financial networks focusing on two important elements of regulatory reforms: collateral requirements and bankruptcy stay rules in over-the-counter (OTC) markets. Under "segregated" collateral requirements, one firm can benefit from the failure of another, the failure frees the committed collateral of the surviving firm giving it additional resources to make other payments. In OTC derivatives markets, similarly, one firm may obtain additional resources upon the failure of another if it terminates its in the money derivatives with the failed entity. Studying contagion in the presence of this real world phenomenon becomes challenging. Our proposed model deviates from the existing network models to capture collateral and accelerated contract termination payments. The model also incorporates fire sales externalities when collateral is held in illiquid assets. We show that asset fire sales increase the risk of contagion if illiquid collateral is seized and sold immediately upon defaults. We also analyze the impact of different bankruptcy stay rules on contagion. Some of our results contrast with the post-crisis stay rules. For instance, we show that when banks are not highly leveraged in terms of their OTC derivatives transactions, which is now the case due to the impact of regulatory reforms, symmetric contract termination in the absence of automatic stays can reduce the risk of contagion.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=122089&date=2019-02-26Student Harmonic Analysis and PDE Seminar (HADES), Feb 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123942&date=2019-02-26
Concentration compactness methods provide a powerful tool for proving global well-posedness and scattering for nonlinear dispersive equations. Once one has a small-data global well-posedness result, one knows that there is some minimal size of the initial data at which global well-posedness and scattering can fail. Then, using a profile decomposition, one can show that there is a minimal blowup solution that is almost periodic. One can then use tools like long-time Strichartz estimates and interaction Morawetz inequalities to rule out these "minimal enemies." I will illustrate this technique by presenting a proof, due to Killip and Visan, of the global well-posedness and scattering for the three-dimensional energy-critical defocusing NLS.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123942&date=2019-02-26Commutative Algebra and Algebraic Geometry: The Fellowship of the Ring, Feb 26
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123751&date=2019-02-26
Codepth is the dual notion to depth, being the greatest length of a coregular sequence for a module, meaning the first element maps the module surjectively, the second is subjective on the kernel of the first, and so on. For a curve in P3, let M be the local cohomology module of the graded coordinate ring with supports in the ideal of the curve. Then the theorem of Hellus says that C is a set theoretic complete intersection if and only if M has codepth 2. This criterion is not directly applicable, so we define the notion of a quasi-cyclic module, which is an increasing limit of cyclic modules. In this talk I will recall the still open problem of whether every irreducible nonsingular curve in P3 is a set theoretic complete intersection, and derive a number of consequences using the concepts introduced above.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=123751&date=2019-02-26