Posted February 3, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Huong Vo, Louisiana State University
TBD
Posted November 21, 2024
Last modified March 5, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 233
Christoph Fischbacher, Baylor University
Non-selfadjoint operators with non-local point interactions
In this talk, I will discuss non-selfadjoint differential operators of the form $i\frac{d}{dx}+V+k\langle \delta,\cdot\rangle$ and $-\frac{d^2}{dx^2}+V+k\langle \delta,\cdot\rangle$, where $V$ is a bounded complex potential. The additional term, formally given by $k\langle \delta,\cdot\rangle$, is referred to as ``non-local point interaction" and has been studied in the selfadjoint context by Albeverio, Cojuhari, Debowska, I.L. Nizhnik, and L.P. Nizhnik. I will begin with a discussion of the spectrum of the first-order operators on the interval and give precise estimates on the location of the eigenvalues. Moreover, we will show that the root vectors of these operators form a Riesz basis. If the initial operator is dissipative (all eigenvalues have nonnegative imaginary part), I will discuss the possibility of choosing the non-local point interaction in such a way that it generates a real eigenvalue even if the potential is very dissipative. After this, I will focus on the dissipative second order-case and show similar results on constructing realizations with a real eigenvalue. Based on previous and ongoing collaborations with Matthias Hofmann, Andrés Lopez Patiño, Sergey Naboko, Danie Paraiso, Chloe Povey-Rowe, Monika Winklmeier, Ian Wood, and Brady Zimmerman.
Posted February 24, 2025
Combinatorics Seminar Questions or comments?
10:30 am Lockett Hall 233
James "Dylan" Douthitt, Louisiana State University
Induced-minor-closed classes of matroids (dissertation defense)
Abstract: A graph is chordal if every cycle of length at least four has a chord. In 1961, Dirac characterized chordal graphs as those graphs that can be built from complete graphs by repeated clique-sums. Generalizing this, we consider the class of simple $GF(q)$-representable matroids that can be built from projective geometries over $GF(q)$ by repeated generalized parallel connections across projective geometries. We show that this class of matroids is closed under induced minors and characterize the class by its forbidden induced minors, noting that the case when $q=2$ is distinctive. Additionally, we show that the class of $GF(2)$-chordal matroids coincides with the class of binary matroids that have none of $M(K_4)$, $M^*(K_{3,3})$, or $M(C_n)$ for $n\geq 4$ as a flat. We also show that $GF(q)$-chordal matroids can be characterized by an analogous result to Rose's 1970 characterization of chordal graphs as those that have a perfect elimination ordering of vertices. We then describe the classes of binary matroids with pairs from the set $\{M(C_4),M(K_4\backslash e),M(K_4),F_7\}$ as excluded induced minors. Additionally, we prove structural lemmas toward characterizing the class of binary matroids that do not contain $M(K_4)$ as an induced minor.
Posted October 14, 2024
Last modified February 28, 2025
Applied Analysis Seminar Questions or comments?
3:30 pm – 4:30 pm Thursday, March 6, 2025 Lockett 232
Alexandru Hening, Texas A&M University
Stochastic Population Dynamics in Discrete Time
I will present a general theory for coexistence and extinction of ecological communities that are influenced by stochastic temporal environmental fluctuations. The results apply to discrete time stochastic difference equations that can include population structure, eco-environmental feedback or other internal or external factors. Using the general theory, I will showcase some interesting examples. I will end my talk by explaining how the population size at equilibrium is influenced by environmental fluctuations.
Posted February 10, 2025
Last modified February 24, 2025
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm 233 Lockett Hall
David Boozer, Indiana University
The combinatorial and gauge-theoretic foam evaluation functors are not the same
Kronheimer and Mrowka have outlined a new approach that could potentially lead to the first non-computer based proof of the four-color theorem. Their approach relies on a functor J-sharp, which they define using gauge theory, from a category of webs in R^3 to the category of finite-dimensional vector spaces over the field of two elements. They have also suggested a possible combinatorial replacement J-flat for J-sharp, which Khovanov and Robert proved is well-defined on a subcategory of planar webs. We exhibit a counterexample that shows the restriction of the functor J-sharp to the subcategory of planar webs is not the same as J-flat.
Posted February 3, 2025
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm
Emmanuel Astante, Louisiana State University
TBD
Posted March 4, 2025
Geometry and Topology Seminar Seminar website
2:30 pm Lockett 233
Maarten Mol, University of Toronto
TBA
Posted February 10, 2025
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Maarten Mol, University of Toronto
TBA: Additional Topology/Rep Theory talk today