The Mathematics Department holds regular seminars on a variety of topics. Please see below for further details.

Seminars

Seminar Meeting Details Title & Abstract
Algebra Seminar
event
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place
MSB 110
Additive number theory meets commutative algebra

Let \(A = \{a_0=0<a_1<\dots<a_{n-1}=d\}\) be a finite set of relatively prime integers. For all \(s\in \mathbb{N}\), the \(s\)-fold sumset of \(A\) is the set \(sA\) of integers obtained by collecting all sums of \(s\) elements in \(A\). On the other hand, given a field \(k\), one can associate with \(A\) the projective monomial curve \(\mathcal{C}_A\) parametrized by (A\), i.e., the Zariski closure of \( \{(v^d:u^{a_1}v^{d-a_1}:\cdots:u^{a_{n-2}}v^{d-a_{n-2}}:u^d) \mid (u:v) \in \mathbb{P}_k^1\} \subset \mathbb{P}_k^{\, n-1} \, .\)
In this talk, I will present some results relating properties of \(\mathcal{C}_A\) to the behavior of the sumsets of \(A\), revealing a new interplay between commutative algebra and additive number theory. This is joint work with P. Gimenez.

Speaker: Mario González Sánchez, Universidad de Valladolid
Data Seminar
event
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place
MSB 110
A fourth moment theorem for estimating subgraph counts in large graphs

Given a large network one is often interested in efficiently estimating various local statistics. In this talk, we'll discuss the distribution of one possible estimator arising from counting monochromatic subgraphs in a random vertex colorings. We focus on the    asymptotic normality of these counts, particularly for monochromatic triangles, and provide new, local influence-based necessary and sufficient conditions.  The conditions we obtain combine ideas from Boolean analysis as well as classical fourth-moment theorems originating from normal approximation results in the Wiener space.

Speaker: Dan Mikulincer (U Washington)
Geometry and Topology Seminar
event
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place
MSB 110
Computing some Gromov-Witten invariants for Hilbert schemes of points on elliptic surfaces
Speaker: Mazen M. Alhwaimel (Qassim University)
Data Seminar
event
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place
MSB 110
Homotopies for variational inference and approximate synthesis

For parameterized systems, one standard problem is to determine the set of parameters which "best" fits given data.  Two examples of this will be summarized in this talk, both of which can be solved using homotopies.  The first is variational inference in which one searches in a parameterized family of probability distributions for a probability distribution that best fits the given data.  The second is synthesizing a linkage whose coupler curve best approximates the given data.  This talk is joint work with Emma Cobian, Fang Liu, and Daniele Schiavazzi (variational inference) and Aravind Baskar and Mark Plecnik (approximate synthesis).

 

Speaker: Jonathan Hauenstein (Notre Dame)
Algebra Seminar
event
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place
MSB 110
Extremal singularities in positive characteristic

What is the most singular possible (reduced) hypersurface in positive characteristic? One answer to this question comes from finding a lower bound on an invariant called the F-pure threshold of a polynomial in terms of its degree. In this talk, I'll introduce the F-pure threshold and then discuss a class of hypersurfaces which obtain a minimal F-pure threshold.  We’ll further investigate some of their surprising algebraic and geometric properties including their connection to surfaces with many lines.  This talk is based on joint work with Zhibek Kadyrsizova, Jennifer Kenkel, Jyoti Singh, Karen E. Smith, Adela Vraciu, and Emily E. Witt.

Speaker: Janet Page, North Dakota State University
Differential Equations Seminar
event
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place
MSB 111
group
Gravity wave-borne vortices

In this talk, we’ll present some recent work on traveling waves in water that carry vortices in their bulk. We show that for any supercritical Froude number (non-dimensionalized wave speed), there exists a continuous one-parameter family of solitary waves with a submerged point vortex in equilibrium. This family bifurcates from an irrotational laminar flow, and, at least for large Froude numbers, it extends up to the development of a surface singularity. These are the first rigorously constructed gravity wave-borne point vortices without surface tension, and notably our formulation allows the free surface to be overhanging. Through a separate numerical study, we find strong evidence that many of the waves do indeed have an overturned air—water interfaces. Finally, we prove that generically one can perform a desingularization procedure to obtain a solitary wave with a submerged hollow vortex. Physically, these can be thought of as traveling waves carrying spinning bubbles of air in their bulk.

We will also discuss some work in progress on the existence of imploding vortex configurations that experience finite-time self-similar collapse.

This is joint work with Ming Chen, Kristoffer Varholm, and Miles Wheeler.
 

Speaker: Samuel Walsh (MU)
Data Seminar
event
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place
Math Sciences Building 110
Density estimation for Gaussian mixture models

Density estimation for Gaussian mixture models is a classical problem in statistics that has applications in a variety of disciplines. Two solution techniques are commonly used for this problem: the method of moments and maximum likelihood estimation. This talk will discuss both methods by focusing on the underlying geometry of each problem.

 

Full seminar calendar: https://sites.google.com/view/mathdatamizzou/home

Speaker: Julia Lindberg
Pre-print Algebra Seminar
event
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place
MSB Room 12
The epsilon multiplicity continued

Part 2 of Stephen’s talk.

Speaker: Stephen Landsittel
Data Seminar
event
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place
Math Sciences Building 110
Generic orbit recovery from invariants of very low degree

Motivated by the multi-reference alignment (MRA) problem and questions in equivariant neural networks we study the problem of recovering the generic orbit in a representation of a finite group from invariant polynomials of degree at most 3. We prove that in many cases of interest these low degree invariants are sufficient to recover the orbit of a generic vector. 

 

Semester seminar calendar: https://sites.google.com/view/mathdatamizzou/home

Speaker: Josh Katz
Pre-print Algebra Seminar
event
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place
MSB Room 12
The History of Asymptotic Multiplicities and the Epsilon Multiplicity

We define the basic machinery of multiplicities and graded families and state some recent theorems on multiplicities (which we will finish proving in part 2).

Speaker: Stephen Landsittel