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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 EL-labeling. We prove that the maximal chain descent order encodes via its linear extensions all shellings of the order complex induced by the EL-labeling strictly including the well-known lexicographic shellings. We show that the standard EL-labeling of the Boolean lattice has maximal chain descent order isomorphic to the type A weak order. We also prove that natural EL-labelings 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 EL-labelings with the expected cover relations including many well-known families of EL-labelings.
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 non-archimedean setting.
Applied Mathematics
- James Murphy, Tufts University
- ZOOM TALK (password the smallest prime > 100) - Towards Intrinsically Low-Dimensional 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 Wasserstein-2 (W2) barycenters of a set of fixed reference measures. Leveraging the Riemannian structure of W2-space, 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 ill-posedness 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 3-braid closures and generic 4-braid 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 3-braid 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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8
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 type-B Coxeter group and the so-called 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 type-B 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 type-B 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 type-B 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 Jean-Christophe 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 Li-Cheng Tsai.
Analysis and PDE
- Alexander Volberg, MSU
- Noncommutative Bohnenblust--Hille inequalities and application to learning the quantum observables
- 02/08/2023
- 4:10 PM - 5:00 PM
- C304 Wells Hall
(Virtual Meeting Link)
- Willie Wai-Yeung Wong (wongwil2@msu.edu)
Bohnenblust--Hille inequalities for Boolean cubes have been proven with dimension-free constants that grow sub-exponentially 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 Bohnenblust--Hille 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 Bohnenblust--Hille inequalities with constants that are dimension-free 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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24
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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28
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.
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