Department of Mathematics Colloquium

 
 


Fall 2017

Tuesdays 4:10 p.m. in Carver 274 - Tea and cookies starting at 3:45 p.m. in Carver 404

The ISU Department of Mathematics Colloquium is organized by

Pablo Raúl Stinga (stinga@iastate.edu)

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October 3

Speaker: Hien Nguyen

Iowa State University

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Upcoming



October 5 (Room: Carver 018)

Speaker: Michael Young

Iowa State University

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October 10

Speaker: Jack H. Lutz

Iowa State University

Title: Who asked us? How the theory of computing answers questions that weren't about computing

Abstract: It is rare for the theory of computing to be used to answer open mathematical questions whose statements do not involve computation or related aspects of logic. This talk discusses recent developments that do exactly this. After a brief review of algorithmic information and dimension, we describe the point-to-set principle (with N. Lutz) and its application to two new results in geometric measure theory. These are (1) N. Lutz and D. Stull's strengthened lower bound on the Hausdorff dimensions of generalized Furstenberg sets, and (2) N. Lutz's extension of the fractal intersection formulas for Hausdorff and packing dimensions in Euclidean spaces from Borel sets to arbitrary sets.


October 12 (Room: Carver 018)

Speaker: Bernard Lidicky

Iowa State University

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October 13 (Room: Carver 202)

Speaker: Ralph McKenzie

Vanderbilt University

Title: P or NP-complete: a very successful application of general algebra to a fundamental graph homomorphism problem

Abstract: With any finite relational structure A we have a computational problem: input a finite structure B of the same signature as A; accept B if and only if there is a homomorphism from B to A. The CSP-dichotomy conjecture of Feder and Vardi states that given any template A (a finite relational structure), the described computational problem either admits a polynomial-time algorithm, or is NP-complete. Feder and Vardi proved that this general conjecture is equivalent to the restricted conjecture where the template is simply a di-graph.
It was observed by Bulatov, Jeavons and Krokhin about year 2000 that study of the polymorphism algebra of the template offers a natural and promising approach to the corresponding CSP problem. There are now two algebraic proofs of the dichotomy conjecture in circulation that are being read and checked by experts in this new field. Whether or not one of these proofs is accepted as valid, the observation of Bulatov, Jeavons and Krokhin has led over the intervening years to great progress in understanding the classification of general CSP problems, while producing an impressive body of deep results in finite universal algebra. 

My talk will sketch developments in both directions, new algorithms for large families of CSP problems, and surprising algebraic results offering unexpected insight into the diversity of deep structures in finite algebras.



October 17

Speaker: Emille Lawrence

University of San Francisco

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October 24

Speaker: Tathagata Basak

Iowa State University

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October 26 (Room: Carver 018)

Speaker: Songting Luo

Iowa State University

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November 7

Speaker: Alicia Prieto Langarica

Youngstown State University

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November 14

Speaker: Yong Zeng

National Science Foundation

Title: Bayesian inference via filtering equations for ultra high frequency data

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Past


September 5

Speaker: Tin-Yau Tam

Auburn University

Title: Orbital geometry - from matrices to Lie groups

Abstract: Given an $n\times n$ matrix $A$, the celebrated Toeplitz-Hausdorff theorem asserts that the classical numerical range $\{x^*Ax: x\in {\mathbb C}^n: x^*x=1\}$ is a  convex set, where ${\mathbb C}^n$ is the vector space of complex $n$-tuples and $x^*$ is the complex conjugate transpose of $x\in {\mathbb C}^n$. Schur-Horn Theorem asserts that the set of the diagonals of Hermitian matrices of a prescribed eigenvalues is the convex hull of the orbit of the eigenvalues under the action of the symmetric groups. These results are about unitary orbit of a matrix. Among interesting generalizations, we will focus our discussion on those in the context of Lie structure, more precisely, compact connected Lie groups and semisimple Lie algebras. Some results on convexity and star-shapedness will be presented.


September 12

Speaker: Dennis Kriventsov

Courant Institute (NYU)

Title: Spectral optimization and free boundary problems

Abstract: A classic subject in analysis is the relationship between the spectrum of the Laplacian on a domain and that domain's geometry. One approach to understanding this relationship is to study domains which extremize some function of their spectrum under geometric constraints. I will give a brief overview of some of these optimization problems and describe the (very few) explicit solutions known. Then I will explain how to approach these problems more abstractly, using tools from the calculus of variations to find solutions. A key difficulty with this approach is showing that the solutions (which are a priori very weak) are actually smooth domains, which I address in some recent work with Fanghua Lin. Our method revolves around relating spectral optimization problems to certain vector-valued free boundary problems of Bernoulli type.



September 19

Speaker: Deanna Haunsperger

Carletton College

Title: Stories from Math Horizons

Abstract: In this talk, Deanna will talk about becoming involved in the Mathematical Association of America as an editor of Math Horizons, some of the cool mathematics she learned in this process, and opportunities for participating in the national mathematical community.



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Spring 2018

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February 13

Daphne Der-Fer Liu

University of South Carolina, Columbia

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March 20

Susan Kelly

University of Wisconsin - La Crosse

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April 10

Shelby Nicole Wilson

Morehouse College

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Fall 2018

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October 16

Vlad Vicol

University of Minnesota

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