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Combinatorics and Graph Theory
 Maya Stein, Universidad de Chile
 Towards a Posa Seymour conjecture for hypergraphs
 01/19/2022
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
A central problem in extremal graph theory is to study degree conditions that force a graph G to contain a copy of some large or even spanning graph F. One of the most classical results in this area is Dirac's theorem on Hamilton cycles. An extension of this theorem is the PosaSeymour conjecture on powers of Hamilton cycles, which has been proved for large graphs by Komlos, Sarkozy and Szemeredi. Extension of these results to hypergraphs, using codegree conditions and tight (powers of) cycles, have been studied by various authors. We give an overview of the known results, and then show a codegree condition which is sufficient for ensuring arbitrary powers of tight Hamilton cycles, for any uniformity. This could be seen as an approximate hypergraph version of the PosaSeymour conjecture. On the way to our result, we show that the same codegree conditions are sufficient for finding a copy of every spanning hypergraph of bounded treewidth which admits a tree decomposition where every vertex is in a bounded number of bags. This is joint work with Nicolas SanhuezaMatamala and Matias PavezSigne.
Algebra
 Yujie Xu, Harvard University
 Normalization in the integral models of Shimura varieties of Hodge type
 01/19/2022
 4:00 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Georgios Pappas (pappasg@msu.edu)
Shimura varieties are moduli spaces of abelian varieties with extra structures. Over the decades, various mathematicians (e.g. Rapoport, Kottwitz, etc.) have constructed nice integral models of Shimura varieties. In this talk, I will discuss some motivic aspects of integral models of Hodge type constructed by Kisin (resp. KisinPappas). I will talk about my recent work on removing the normalization step in the construction of such integral models, which gives closed embeddings of Hodge type integral models into Siegel integral models. I will also mention an application to toroidal compactifications of such integral models.

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Applied Mathematics
 Ilse Ipsen , North Carolina State University
 BayesCG: A probabilistic numeric linear solver
 01/20/2022
 2:30 PM  3:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
We present the probabilistic numeric solver BayesCG, for solving linear systems with real symmetric positive definite coefficient matrices. BayesCG is an uncertainty aware extension of the conjugate gradient (CG) method that performs solutionbased inference with Gaussian distributions to capture the uncertainty in the solution due to early termination. Under a structure exploiting `Krylov' prior, BayesCG produces the same iterates as CG. The Krylov posterior covariances have low rank, and are maintained in factored form to preserve symmetry and positive semidefiniteness. This allows efficient generation of accurate samples to probe uncertainty in subsequent computations.

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Geometry and Topology
 Elijah Bodish, University of Oregon
 Rank 2 JonesWenzl projectors
 01/25/2022
 2:00 PM  3:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
In 1932 RumorTellerWeyl observed that endomorphism algebras of tensor products of the vector representation for sl_2 can be described by (linear combinations of) crossingless matching diagrams. This is now known under the moniker: TemperleyLieb algebra. The JonesWenzl projectors are linear combinations of crossingless matching diagrams which describe the idempotent projecting to the symmetric powers. These projectors satisfy recursive formulas which can aid in their computation, and have proved useful in representation theory, knot theory, the study of subfactors, and categorification.
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In his 1996 paper “Rank 2 spiders for Lie algebras", Kuperberg defined an analogue of TempeleyLieb algebras for each rank 2 simple Lie algebra (i.e. sl_3, sp_4, and g_2). He also proved that the analogues of the JonesWenzl projectors exist for rank 2 as well. Then D. Kim and later B. Elias found recursive descriptions of these projectors in the case of sl_3, and Elias gave a conjecture about how these recursions may look for sl_n. The most interesting aspect of this conjecture is that the coefficients in the projectors, which are by definition solutions to some complicated recursive formula, are actually described compactly by formulas analogous to the Weyl dimension formula.
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In my talk I will review the above background material and then discuss my work on finding recursive descriptions of the projectors in the case of sp_4 and g_2 . The case of sp_4 appears in arxiv:2102.05186 and the case of g_2, which is joint with Haihan Wu from UC Davis, appears in arXiv:2112.01007. I will also discuss how the rank 2 projectors fit into the frame work of Elias’s conjecture in type A, and suggest how the whole story may generalize to other Lie algebras.

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Algebra
 Clément Dupont, Université de Montpellier
 On periods and their Galois theory (note unusual time!)
 01/26/2022
 12:40 PM  1:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Preston Wake (wakepres@msu.edu)
I will give a leisurely introduction to the modern study of periods via the cohomology of algebraic varieties and the theory of motives. Many examples will be given, with a particular focus on the idea of a Galois theory of periods that generalizes the classical Galois theory of algebraic numbers. If time allows, I will review work in progress (with Francis Brown, Javier Fresán, and Matija Tapušković) on the Galois theory of algebraic Mellin transforms — or maybe just the beta function.

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Applied Mathematics
 Yong Sheng Soh, National University of Singapore
 Learning Sparse Representations with Symmetries
 01/27/2022
 3:30 AM  3:30 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
In this talk, we consider the problem of learning sparse representations for data under the constraint that the representation satisfies some desired invariance. The problem of learning sparse representations is more typically referred to as dictionary learning in the literature, and the specific task we consider can be viewed as an extension of the convolutional dictionary learning problem.
Building on ideas from group representation theory, harmonic analysis, and convex geometry, we describe an endtoend recipe for learning such data representations that are invariant to a fairly broad family of symmetries, and in particular, continuous ones. Our techniques draw connections between our learning problem and the geometric problem of fitting appropriately parameterized orbitopes to data. Spectrahedral descriptions of certain orbitopes based on Toeplitz positive semidefinite matrices feature prominently in our work.
Analysis and PDE
 Jérémie Szeftel, Laboratoire JacquesLouis Lions de Sorbonne Université
 The nonlinear stability of Kerr for small angular momentum
 01/27/2022
 10:00 AM  11:00 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Willie WaiYeung Wong (wongwil2@msu.edu)
I will introduce the celebrated black hole stability conjecture according to which the Kerr family of metrics are stable as solutions to the Einstein vacuum equations of general relativity. I will then discuss the history of this problem, including a recent work on the resolution of the black hole stability conjecture for small angular momentum.
Student Algebra Seminar

 Student Algebra Seminar orientation meeting
 01/27/2022
 2:00 PM  3:00 PM
 Online (virtual meeting)
 Owen GaryDennis Ekblad (ekbladow@msu.edu)
No abstract available.

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Student Analysis Seminar
We'll get to know one another in the beginning, see who's willing to give a talk in the future and try to organise a little bit in general.
Then, I'll start with a brief review of normal families before we dwell into the world of fractals.

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