# 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) _________________________________________________________________________________________________________ October 3 Speaker: Hien Nguyen Iowa State University Title: Abstract: _________________________________________________________________________________________________________ Upcoming October 5 (Room: Carver 018) Speaker: Michael Young Iowa State University Title: Abstract: 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 Title: Abstract: 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 Title: Abstract: October 24 Speaker: Tathagata Basak Iowa State University Title:  Abstract: October 26 (Room: Carver 018) Speaker: Songting Luo Iowa State University Title: Abstract:   November 7 Speaker: Alicia Prieto Langarica Youngstown State University Title: Abstract: November 14 Speaker: Yong Zeng National Science Foundation Title: Bayesian inference via filtering equations for ultra high frequency data Abstract: _________________________________________________________________________________________________________ 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. _________________________________________________________________________________________________________ Spring 2018 _________________________________________________________________________________________________________   February 13 Daphne Der-Fer Liu University of South Carolina, Columbia Title: Abstract: March 20 Susan Kelly University of Wisconsin - La Crosse Title: Abstract: April 10 Shelby Nicole Wilson Morehouse College Title: Abstract: Date Speaker University Title: Abstract: _________________________________________________________________________________________________________ Fall 2018 _________________________________________________________________________________________________________   October 16 Vlad Vicol University of Minnesota Title: Abstract: