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Combinatorics and Graph Theory
- Sergi Elizalde, Dartmouth College
- Descents on quasi-Stirling permutations
- 01/20/2021
- 3:00 PM - 3:50 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Bruce E Sagan (bsagan@msu.edu)
Stirling permutations were introduced by Gessel and Stanley to give a combinatorial interpretation of certain polynomials related to Stirling numbers. A very natural extension of Stirling permutations are quasi-Stirling permutations, which are in bijection with labeled rooted plane trees. Archer et al. introduced these permutations, and conjectured that there are $(n+1)^{n-1}$ quasi-Stirling permutations of size $n$ having $n$ descents.
In this talk we prove this conjecture. More generally, we give the generating function for quasi-Stirling permutations by the number of descents, which turns out to satisfy a beautiful equation involving Eulerian polynomials. We show that some of the properties of descents on usual permutations and on Stirling permutations have an analogue for quasi-Stirling permutations.
Finally, we extend our results to a one-parameter family of permutations, called $k$-quasi-Stirling permutations, which are in bijection with certain decorated trees.
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Applied Mathematics
- Daniel Kane, University of California, San Diego
- Point Location and Active Learning
- 01/21/2021
- 2:30 PM - 3:30 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Olga Turanova (turanova@msu.edu)
In the point location problem one is given a hyperplane arrangement and an unknown point. By making linear queries about that point one wants to determine which cell of the hyperplane arrangement it lies in. This problem has an unexpected connection to the problem in machine learning of actively learning a halfspace. We discuss these problems and their relationship and provide a new and nearly optimal algorithm for solving them.
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Student Number Theory
- Zheng Xiao, MSU
- Extensions of function fields
- 01/22/2021
- 5:00 PM - 6:00 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Zheng Xiao (xiaozhen@msu.edu)
No abstract available.
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Conversations among Colleagues
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- Online large lectures and coordinated courses - challenges and opportunities
- 01/26/2021
- 10:00 AM - 11:00 AM
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(Virtual Meeting Link)
- Tsvetanka Sendova (tsendova@msu.edu)
No abstract available.
Geometry and Topology
- Matt Stoffregen, MSU
- Surgery Exact Triangles in Involutive Floer homology
- 01/26/2021
- 2:50 PM - 3:40 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Honghao Gao (gaohongh@msu.edu)
We'll sketch the definition of the involutive Heegaard Floer homology constructed by Hendricks-Manolescu, and then explain how this homology theory behaves under surgery. As a consequence, we can use the surgery formula to construct three-manifolds which are not homology cobordant to any combination of Seifert fiber spaces. This is joint work Kristen Hendricks, Jen Hom and Ian Zemke.
Colloquium
- Luis Silvestre, University of Chicago
- Integro-differential diffusion and the Boltzmann equation
- 01/26/2021
- 4:30 PM - 5:30 PM
- Online (virtual meeting)
- Aaron D Levin (levina@msu.edu)
Integro-differential equations have been a very active area of research in the last 20 years. In this talk we will explain what they are and in what sense they are similar to more classical parabolic partial differential equations. We will discuss results on regularity estimates for the Boltzmann equation in this context.
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Combinatorics and Graph Theory
- Joshua Swanson, UCSD
- DUSTPAN distributions as limit laws for Mahonian statistics on forests
- 01/27/2021
- 3:00 PM - 3:50 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Bruce E Sagan (bsagan@msu.edu)
Building on work of Stanley and Björner-Wachs, we study the distribution of certain Mahonian statistics on several families of posets, including the major index on linear extensions of forests. We show that the resulting standardized distributions are often asymptotically normal. However, in certain regimes, we must introduce a new, closed family of continuous probability distributions called DUSTPAN distributions which simultaneously generalize the Irwin-Hall and normal distributions. In the case of forests, we use graph-theoretic statistics like height and elevation to completely determine the precise limit laws. This leads to some natural open questions about the distribution of the height of such forests.
Joint work with Sara Billey (https://arxiv.org/abs/2010.12701) building on earlier joint work with Sara Billey and Matjaž Konvalinka (https://arxiv.org/abs/1905.00975).
Algebra
- Vaidehee Thatte, SUNY Binghamton
- Arbitrary Valuation Rings and Wild Ramification
- 01/27/2021
- 4:00 PM - 5:00 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Preston Wake (wakepres@msu.edu)
We aim to develop ramification theory for arbitrary valuation fields, extending the classical theory of complete discrete valuation fields with perfect residue fields. By studying wild ramification, we hope to understand the mysterious phenomenon of the $\textit{defect}$ (or ramification deficiency) unique to the positive residue characteristic case and is one of the main obstacles in obtaining resolution of singularities.
Extensions of degree $p$ in residue characteristic $p>0$ are building blocks of the general case. We present a generalization of ramification invariants for such extensions. These results enable us to construct an upper ramification filtration of the absolute Galois group of Henselian valuation fields (joint with K.Kato).
Student Geometry/Topology
- Keshav Sutrave, Michigan State University
- An intro to Riemann surfaces: What your complex analysis prof. doesn’t want you to know
- 01/27/2021
- 4:00 PM - 5:00 PM
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- Danika Van Niel (vannield@msu.edu)
Riemann surfaces blend together complex analysis, geometry, and topology (and then eventually connect to PDE’s, algebraic geometry & number theory, and probably everything else).
I will only scratch the surface by introducing them, as well as the notions of branched covering, monodromy, and the Riemann-Hurwitz formula.
Zoom link: https://msu.zoom.us/j/91485321701
Password: SGTS
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Applied Mathematics
- Zuowei Shen, National University of Singapore
- Deep Approximation via Deep Learning
- 01/28/2021
- 3:30 AM - 4:30 AM
- Online (virtual meeting)
(Virtual Meeting Link)
- Olga Turanova (turanova@msu.edu)
The primary task of many applications is approximating/estimating a function through samples drawn from a probability distribution on the input space. The deep approximation is to approximate a function by compositions of many layers of simple functions, that can be viewed as a series of nested feature extractors. The key idea of deep learning network is to convert layers of compositions to layers of tuneable parameters that can be adjusted through a learning process, so that it achieves a good approximation with respect to the input data. In this talk, we shall discuss mathematical theory behind this new approach and approximation rate of deep network; how this new approach differs from the classic approximation theory, and how this new theory can be used to understand and design deep learning network.
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Student Algebra Seminar
- Nick Rekuski, MSU
- Etale Cohomology I: Preliminary
- 01/29/2021
- 1:00 PM - 2:00 PM
- Online (virtual meeting)
- Chuangtian Guan (guanchua@msu.edu)
No abstract available.
Student Number Theory
- Zheng Xiao, MSU
- $ef$ Theorem, discriminant and different in function fields
- 01/29/2021
- 5:00 PM - 6:00 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Zheng Xiao (xiaozhen@msu.edu)
No abstract available.
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