Mathematics
http://events.berkeley.edu/index.php/calendar/sn/math.html
Upcoming EventsCombinatorics Seminar, Oct 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129014&date=2019-10-14
Various pattern-avoiding 0/1-fillings of Ferrers diagrams are in bijection with permutations, where several statistics on the permutations translate into statistics on the filled diagrams (or tableaux). Two such bijections from permutations are to the Le-tableaux arising from Postnikov's work on the nonnegative Grassmannian and the EW-tableaux originally defined in Ehrenborg and van Willigenburg's work on Ferrers graphs. These tableaux and permutations are closely connected to the Partially Asymmetric Exclusion Process and the Abelian Sandpile Model, respectively. I will describe the underlying bijections and some of their properties, and show how the "transformation fondamentale" of Foata and Schützenberger translates between the permutations in question, thus providing a surprising connection between these two physics models. This is joint work with Mark Dukes, Thomas Selig and Jason P. Smith.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129014&date=2019-10-14Differential Geometry Seminar, Oct 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=128811&date=2019-10-14
Given a Riemannian manifold $M$, harmonic forms induce a map $H^*(M;\mathbb R) \to \Omega ^*(M)$ which is in general not multiplicative. Manifolds for which it is are called geometrically formal and besides compact symmetric spaces few examples are known. A different picture emerges when we ask about the existence of some multiplicative map $H^*(M;\mathbb R) \to \Omega ^*(M)$. For example, such a map exists for $(\mathbb {CP} )^{\sharp 3}$ but not $(\mathbb {CP}^2)^{\sharp 4}$. Unlike geometric formality, this property is purely topological, in fact an invariant of rational homotopy type. It also has a number of geometric and topological consequences and equivalent formulations. This is joint work with Sasha Berdnikov.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=128811&date=2019-10-14Arithmetic Geometry and Number Theory RTG Seminar, Oct 14
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129034&date=2019-10-14
The set of irreducible components of an affine Deligne-Lusztig variety is interesting for many applications related to Shimura varieties. A natural symmetry group J acts on this set, and it is desirable to determine the orbits and the stabilizers of this action. In joint work with Rong Zhou, we prove a formula for the number of orbits, earlier conjectured by Miaofen Chen and Xinwen Zhu. In joint work in progress with Xuhua He and Rong Zhou, we show that all the stabilizers are very special parahorics. As an application, we deduce a formula for the number of irreducible components in the basic Newton stratum in Shimura varieties.<br />
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In the pre-talk, I will give a crash course on the unramified Hecke algebra and different bases of it.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129034&date=2019-10-14Seminar 217, Risk Management: Testing for strategic interaction in social and economic network formation, Oct 15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=126671&date=2019-10-15
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=126671&date=2019-10-15Combinatorics Reading Seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129083&date=2019-10-16
This talk will focus on combinatorial objects called ice models, which arise in statistical mechanics. We will start by exploring the relationship between semi-standard Young tableaux and Gelfand-Tsetlin patterns, and see how the Shur polynomial can be defined in terms of those objects. In general, given rules for a tableaux representing a branching rule for GL(n, C), we define a bijection between the tableaux and Gelfand-Tsetlin patterns. Restricting our attention to only strict Gelfand-Tsetlin patterns and the corresponding so-called “shifted” tableaux, we can construct a certain ice model in bijection with those objects. Assigning appropriate weights to the vertices of the resulting ice model, we obtain a partition function that is equal to the product of the type A deformation formula and the character of GL(n,C), which is precisely the Shur polynomial. We will sketch a proof that the weights proposed by Brubaker, Bump and Friedberg give the desired equation using the star-triangle identity.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129083&date=2019-10-16Topology Seminar (Introductory Talk), Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=128865&date=2019-10-16
This pre-talk explains some of the background behind the asymptotics of ECH capacities and its subleading estimate. Firstly this includes an outline of Taubes's isomorphism between embedded contact homology (ECH) and monopole Floer homology (HM). Next we describe the eta invariant of Atiyah-Patodi-Singer, some of its analytic properties and its relationship with the rational Q-grading on HM.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=128865&date=2019-10-16Concentration of measure phenomenon in sub-critical exponential random graphs, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129011&date=2019-10-16
The exponential random graph model (ERGM) is a central object in the study of clustering properties in social networks as well as canonical ensembles in statistical physics. It is a version of the well known Erd˝os-R´enyi graphs, obtained by tilting according to the subgraph counting Hamiltonian. Despite its importance in the theory of random graphs, lots of fundamental questions have remained unanswered owing to the lack of exact solvability. In this talk, I will introduce a series of new concentration of measure results for the ERGM throughout the entire sub-critical phase, including a Poincaré inequality, Gaussian concentration, and a central limit theorem. Joint work with Shirshendu Ganguly.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129011&date=2019-10-16Berkeley Number Theory Learning Seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=128334&date=2019-10-16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=128334&date=2019-10-16Flexibility, Interpretability, and Scalability in Time Series Modeling, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=128804&date=2019-10-16
We are increasingly faced with the need to analyze complex data streams; for example, sensor measurements from wearable devices have the potential to transform healthcare. Machine learning—and moreover deep learning—has brought many recent success stories to the analysis of complex sequential data sources, including speech, text, and video. However, these success stories involve a clear prediction goal combined with a massive (benchmark) training dataset. Unfortunately, many real-world tasks go beyond simple predictions, especially in cases where models are being used as part of a human decision-making process or medical intervention. Such complex scenarios necessitate notions of interpretability and measures of uncertainty. Furthermore, in aggregate the datasets might be large, but we might have limited data about an individual, requiring parsimonious modeling approaches.<br />
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In this talk, we first discuss how sparsity-inducing penalties can be deployed on the weights of deep neural networks to enable interpretable structure learning, in addition to yielding more parsimonious models that better handle limited data scenarios. We then turn to Bayesian dynamical modeling of individually sparse data streams, flexibly sharing information and accounting for uncertainty. Finally, we discuss our recent body of work on scaling computations to massive time series, mitigating bias in stochastic gradient based algorithms applied to sequential data sources. Throughout the talk, we provide analyses of activity, neuroimaging, genomic, housing and homelessness data sources.<br />
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Bio: Emily Fox is an Associate Professor in the Paul G. Allen School of Computer Science & Engineering and Department of Statistics at the University of Washington, and is the Amazon Professor of Machine Learning. Currently, she is also Director of Health AI at Apple. She received her Ph.D. in EECS from MIT, with her dissertation being awarded the Leonard J. Savage Thesis Award in Applied Methodology and MIT EECS Jin-Au Kong Outstanding Doctoral Thesis Prize. She has also been awarded a Presidential Early Career Award for Scientists and Engineers (2017), Sloan Research Fellowship (2015), ONR Young Investigator award (2015), and NSF CAREER award (2014). Her research interests are in large-scale dynamic modeling and computations, with a focus on Bayesian methods and applications in health and computational neuroscience.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=128804&date=2019-10-16Topology Seminar, Oct 16
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=128814&date=2019-10-16
On a closed, contact three manifold the asymptotics of its ECH spectrum are known to recover the contact volume. This has applications to the existence of at least two, and in some cases two or infinitely many, Reeb orbits as well as the density of the union of periodic Reeb orbits for generic contact forms. In this talk, we improve the asymptotic formula for ECH spectrum with a subleading estimate. This has applications to a Weyl law for the ECH spectrum and the region of analyticity of the ECH zeta function.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=128814&date=2019-10-163-Manifold Seminar, Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129117&date=2019-10-17
Much of what we know about mapping class groups of compact surfaces stems from their well known classification. In recent years, much effort has been directed towards understanding "big" mapping class groups, i.e. the mapping class groups of surfaces of infinite type. In this talk, we'll walk through Ian Richards' proof that such surfaces are completely classified by their space of ends. We'll define the space of ends and see some rather unintuitive consequences of this result.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129117&date=2019-10-17RTMP Seminar, Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129119&date=2019-10-17
Starting with work of Seidel and Thomas, there has been a great interest in the construction of faithful actions of various classes of groups on derived categories (braid groups, fundamental groups of hyperplane arrangements, mapping class groups). We will describe a general construction of this sort in the setting of algebraic 2-Calabi-Yau triangulated categories. It is applicable to categories coming from algebraic geometry, cluster algebras and topology. To each algebraic 2-Calabi-Yau category, we associate a groupoid, defined in an intrinsic homological way, and then construct a representation of it by derived equivalences. In a certain general situation we prove that this action is faithful and that the green green groupoid is isomorphic to the Deligne groupoid of a hyperplane arrangement. This applies to the 2-Calabi-Yau categories arising from algebraic geometry. We will also illustrate this construction for categories coming from cluster algebras, where one gets categorical actions of braid groups. This is a joint work with Peter Jorgensen (Newcastle University).http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129119&date=2019-10-17Mathematics Department Colloquium, Oct 17
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=128185&date=2019-10-17
It has been known for some time that the free convolution of two nontrivial probability measures on the real line has few point masses. In fact, every point mass of the convolution is uniquely written as the sum of two point masses of the original measures, and the two points in question are obtained as boundary values of the analytic subordination functions that arise in this context. This is easily interpreted in terms of sums of independent sufficiently symmetric large random matrices. Subordination is also useful in determining outlying eigenvalues of "spiked" matrix models. The consideration of more complicated functions of two (or more) independent random matrices requires the free convolution of operator-valued probability distributions and the study of the "point masses" of such distributions. We will discuss the background of these questions as well as some progress coming from joint work with S. Belinschi and W. H. Liu.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=128185&date=2019-10-17BLISS Seminar: Spectral graph matching and regularized quadratic relaxations, Oct 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129032&date=2019-10-18
Given two unlabeled, edge-correlated graphs on the same set of vertices, we study the “graph matching” problem of identifying the unknown mapping from vertices of the first graph to those of the second. This amounts to solving a computationally intractable quadratic assignment problem. We propose a new spectral method, which computes the eigendecomposition of the two graph adjacency matrices and returns a matching based on the pairwise alignments between all eigenvectors of the first graph with all eigenvectors of the second. Each alignment is inversely weighted by the distance between the corresponding eigenvalues. This spectral method can be equivalently viewed as solving a regularized quadratic programming relaxation of the quadratic assignment problem. We show that for a correlated Erdos-Renyi model, this method can return the exact matching with high probability if the two graphs differ by at most a 1/polylog(n) fraction of edges, both for dense graphs and for sparse graphs with at least polylog(n) average degree. Our analysis exploits local laws for the resolvents of sparse Wigner matrices. Based on joint work with Zhou Fan, Cheng Mao, Yihong Wu, all at Yale.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129032&date=2019-10-18Logic Colloquium, Oct 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=128940&date=2019-10-18
The question of categoricity of the universal cover of certain algebraic varieties begun with Zilber’s study of the complex exponential function, and his methods have allowed people to study the question on other arithmetic varieties. In this talk we will consider the case of Shimura varieties, and we will see how some ideas from model theory and the classification of abstract elementary classes, can have explicit reformulations in terms of arithmetic geometry.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=128940&date=2019-10-18Student Arithmetic Geometry Seminar, Oct 18
http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129120&date=2019-10-18
We will give a brief overview of the Hodge bundle and Faltings height. We will do some explicit computations and also motivate their research by stating some important results and conjectures in Diophantine geometry.http://events.berkeley.edu/index.php/calendar/sn/math.html?event_ID=129120&date=2019-10-18