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1
Combinatorics and Graph Theory
 Stephen Lacina, University of Oregon
 Maximal Chain Descent Orders
 02/01/2023
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
We introduce a new partial order called the maximal chain descent order on the maximal chains of any finite, bounded poset with an ELlabeling. We prove that the maximal chain descent order encodes via its linear extensions all shellings of the order complex induced by the ELlabeling strictly including the wellknown lexicographic shellings. We show that the standard ELlabeling of the Boolean lattice has maximal chain descent order isomorphic to the type A weak order. We also prove that natural ELlabelings of intervals in Young's lattice give maximal chain descent orders isomorphic to partial orders on the standard Young tableaux or standard skew tableaux of a fixed shape given by swapping certain entries. We additionally show that the cover relations of maximal chain descent orders are generally more subtle than one might first expect, but we characterize the ELlabelings with the expected cover relations including many wellknown families of ELlabelings.
Algebra Learning Seminar
 Igor Rapinchuk, MSU
 Profinite groups and infinite Galois theory
 02/01/2023
 3:00 PM  4:00 PM
 C329 Wells Hall
 Igor Rapinchuk (rapinchu@msu.edu)
No abstract available.

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Student Number Theory
 Jie Yang, MSU
 Potentially orthonormalizable modules
 02/02/2023
 2:00 PM  3:00 PM
 C204A Wells Hall
 Jie Yang (yangji79@msu.edu)
I will discuss basics of potentially orthonormalizable modules and some related concepts, which are preliminaries for the theory of Fredholm's determinant of compact operators in nonarchimedean setting.
Applied Mathematics
 James Murphy, Tufts University
 ZOOM TALK (password the smallest prime > 100)  Towards Intrinsically LowDimensional Models in Wasserstein Space: Geometry, Statistics, and Learning
 02/02/2023
 2:30 PM  3:30 PM
 C304 Wells Hall
 Mark A Iwen ()
We consider the problems of efficient modeling and representation learning for probability distributions in Wasserstein space. We consider a general barycentric coding model in which data are represented as Wasserstein2 (W2) barycenters of a set of fixed reference measures. Leveraging the Riemannian structure of W2space, we develop a tractable optimization program to learn the barycentric coordinates when given access to the densities of the underlying measures. We provide a consistent statistical procedure for learning these coordinates when the measures are accessed only by i.i.d. samples. Our consistency results and algorithms exploit entropic regularization of the optimal transport problem, thereby allowing our barycentric modeling approach to scale efficiently. We also consider the problem of learning reference measures given observed data. Our regularized approach to dictionary learning in Wasserstein space addresses core problems of illposedness and in practice learns interpretable dictionary elements and coefficients useful for downstream tasks. Applications to image and natural language processing will be shown throughout the talk.

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Geometry and Topology
 Amitesh Datta, Princeton University
 Does the Jones polynomial of a knot detect the unknot? A novel approach via braid group representations and class numbers of number fields.
 02/07/2023
 3:30 PM  4:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Peter Kilgore Johnson (john8251@msu.edu)
How good of an invariant is the Jones polynomial? The question is closely tied to studying braid group representations since the Jones polynomial can be defined as a (normalized) trace of a braid group representation.
In this talk, I will present my work developing a new theory to precisely characterize the entries of classical braid group representations, which leads to a generic faithfulness result for the Burau representation of B_4 (the faithfulness is a longstanding question since the 1930s and is equivalent to whether B_4 is a group of 3 x 3 matrices). In forthcoming work, I use this theory to furthermore explicitly characterize the Jones polynomial of all 3braid closures and generic 4braid closures. I will also describe my work which uses the class numbers of quadratic number fields to show that the Jones polynomial detects the unknot for 3braid links  this work also answers (in a strong form) a question of Vaughan Jones.
I will discuss all of the relevant background from scratch and illustrate my techniques through simple examples.

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Combinatorics and Graph Theory
 Wenjie Fang, Graz University of Technology
 Parabolic Tamari Lattices in Linear Type B
 02/08/2023
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Bruce E Sagan (bsagan@msu.edu)
We study parabolic aligned elements associated with the typeB Coxeter group and the socalled linear Coxeter element. These elements were introduced algebraically in (Mühle and Williams, 2019) for parabolic quotients of finite Coxeter groups and were characterized by a certain forcing condition on inversions. We focus on the typeB case and give a combinatorial model for these elements in terms of pattern avoidance. Moreover, we describe an equivalence relation on parabolic quotients of the typeB Coxeter group whose equivalence classes are indexed by the aligned elements. We prove that this equivalence relation extends to a congruence relation for the weak order. The resulting quotient lattice is the typeB analogue of the parabolic Tamari lattice introduced for type A in (Mühle and Williams, 2019). These lattices have not appeared in the literature before. As work in progress, we will also talk about various combinatorial models and bijections between them. Joint work with Henri Mühle and JeanChristophe Novelli.
Probability
 Yier Lin, University of Chicago
 Some recent progress in the weak noise theory of the KPZ equation
 02/08/2023
 3:00 PM  3:50 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Konstantin Matetski (matetski@msu.edu)
In this talk, we will study the Freidlin–Wentzell LDP for the KPZ equation using the variational principle. Such an approach goes under the name of the weak noise theory in physics. We will explain how to extract various limits of the most probable shape of the KPZ equation in the setting of the Freidlin–Wentzell LDP. Some future directions will also be discussed at the end. The talk is based on several joint works with Pierre Yves Gaudreau Lamarre and LiCheng Tsai.
Analysis and PDE
 Alexander Volberg, MSU
 Noncommutative BohnenblustHille inequalities and application to learning the quantum observables
 02/08/2023
 4:10 PM  5:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Willie WaiYeung Wong (wongwil2@msu.edu)
BohnenblustHille inequalities for Boolean cubes have been proven with dimensionfree constants that grow subexponentially in the degree (Defant—Mastylo—Peres). Such inequalities have found great applications in learning low degree Boolean functions (Eskenazis—Ivanisvili). Motivated by learning quantum observables, a quantum counterpart of BohnenblustHille inequality for Boolean cubes was recently conjectured in Cambyse Rouz\’e, Melchior Wirth, and Haonan Zhang: ``Quantum Talagrand, KKL and Friedgut’s theorems and the learnability of quantum Boolean functions.” arXiv preprint, arXiv:2209.07279, 2022.
Haonan Zhang and myself prove such noncommutative BohnenblustHille inequalities with constants that are dimensionfree and of exponential growth in the degree. As applications, we study learning problems of quantum observables.
(Speaker will present remotely)

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Conversations among Colleagues
 Round Table Discussion, MSU
 Flexibility at Scale: Makeup Exams and Syllabus policies
 02/09/2023
 11:00 AM  12:00 PM
 D101 Wells Hall
 Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.

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Algebra
 Keerthi Madapusi Pera, Boston College
 Derived cycles on Shimura varieties
 02/13/2023
 3:00 PM  4:00 PM
 C304 Wells Hall
 Georgios Pappas (pappasg@msu.edu)
I’ll explain how methods from derived algebraic geometry can be applied to give a uniform definition of special cycle classes on integral models of Shimura varieties of Hodge type, verifying some consequences of Kudla’s conjectures on the modularity of generating series of cycles on Shimura varieties of Hermitian type.

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Geometry and Topology
 Renaud Detcherry, Institut de Mathématiques de Bourgogne
 TBA
 02/14/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Efstratia Kalfagianni (kalfagia@msu.edu)
No abstract available.

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Geometry and Topology
 Ian Montague , Brandeis University
 TBA
 02/21/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Peter Kilgore Johnson (john8251@msu.edu)
No abstract available.

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Colloquium
 Brendan Hassett, Brown University
 TBA
 02/23/2023
 4:10 PM  5:00 PM
 Online (virtual meeting)
 Joseph Waldron (waldro51@msu.edu)
No abstract available.

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Applied Mathematics
 Yuehaw Khoo, U Chicago
 TBA
 02/24/2023
 4:00 PM  5:00 PM
 C304 Wells Hall
 Mark A Iwen (iwenmark@msu.edu)
TBA

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Algebra
 Michail Savvas, University of Texas
 TBA
 02/27/2023
 3:00 PM  4:00 PM
 C304 Wells Hall
 Francois Greer (greerfra@msu.edu)
No abstract available.

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Geometry and Topology
 Ryan Stees, Indiana University
 TBA
 02/28/2023
 2:00 PM  3:00 PM
 C304 Wells Hall
 Peter Kilgore Johnson (john8251@msu.edu)
No abstract available.
