Posted March 28, 2024
Faculty Meeting Questions or comments?
2:30 pm – 3:20 pm ZoomMeeting of Tenured Faculty
Posted November 14, 2023
Last modified March 26, 2024
Algebra and Number Theory Seminar Questions or comments?
3:20 pm – 4:10 pm Lockett 233 or click here to attend on Zoom
Micah Milinovich, University of Mississippi
Biases in the gaps between zeros of Dirichlet L-functions
We describe a family of Dirichlet L-functions that provably have unusual value distribution and experimentally have a significant and previously undetected bias in the distribution of gaps between their zeros. This has an arithmetic explanation that corresponds to the nonvanishing of a certain Gauss-type sum. We give a complete classification of the characters for when these sums are nonzero and count the number of corresponding characters. It turns out that this Gauss-type sum vanishes for 100% of primitive Dirichlet characters, so L-functions in our newly discovered family are rare (zero density set amongst primitive characters). If time allows, I will also describe some newly discovered experimental results concerning a "Chebyshev-type" bias in the gaps between the zeros of the Riemann zeta-function. This is joint work with Jonathan Bober (Bristol) and Zhenchao Ge (Waterloo).
Posted January 18, 2024
Last modified April 2, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Huong Vo, Louisiana State University
The Solomon-Tits theorem
The Solomon-Tits theorem states that a spherical Tits building over a field is homotopy equivalent to a wedge of spheres of the appropriate dimension. In this talk, we will go over some specific examples that show the theorem using PL Morse Theory.
Posted December 1, 2023
Last modified April 1, 2024
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Neal Stoltzfus, Mathematics Department, LSU
The Heart of the Braid Group
The ubiquitous braid group can be approached from many perspectives (algebraic geometrically, combinatorially, geometric group theoretically). This talk will concentrate on developing a description of the image of the known injective (finite dimensional faithful) representation of Lawrence/Krammer/Bigelow. Recalling Artin's faithful infinite dimensional representation and his "combing of pure braids", we first develop an analog for the (unfaithful) Burau representation case using covering spaces, local coefficients and the Reidemeister homotopical intersection theory for the braid action on one-point configurations. Next we introduce the braid action on the (unordered) two-point configuration space utilized by Krammer and Bigelow. For an easier description and computation, we will utilize the two-fold covering space of ordered pair configurations. The complements of these (discriminantal) arrangements are fibrations whose fundamental groups are semi-direct products from pure braid combing. Computing Blanchfield duality of the complements of open tubular neighborhood of the hyperplane arrangements we determine the first restriction on the image of the LKB representation: Hermitian form invariance under the intersection form discovered by Budney and Song. Additional conditions are determined by arithmetic monoidal conditions arising from matrix invariants over polynomial monoids, N[q, 1-q, t] related to (Dehornoy-Paris-Garside) group structures within the braid group. We conclude with a discussion of potential applications.
Posted March 28, 2024
Combinatorics Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233 (Simulcasted via Zoom)
Laszlo Szekely, University of South Carolina
Tanglegrams with the largest crossing number
A tanglegram consists of two binary trees with the same number of leaves, a left binary tree and a right binary tree, and a perfect matching between the leaves of the two trees. The size of a tanglegram is the number of matching edges. Tanglegrams are drawn in a special way. Leaves of the left tree must be on the line $x=0$, leaves of the right tree must be on the line $x=1$, the left binary tree is a plane tree in the halfplane $x\leq 0$, the right binary tree is a plane tree in the halfplane $x\geq 1$, and the perfect matching must be drawn in straight line segments. Such a drawing is called a layout of the tanglegram. The crossing number of a layout is the number of unordered pairs of matching edges that cross, while The crossing number of a tanglegram is the least number of crossings in layouts of this tanglegram. It is easy to see that the crossing number of a size $n$ tanglegram is at most $\binom{n}{2}$. Anderson, Bai, Barrera-Cruz, Czabarka, Da Lozzo, Hobson, Lin, Mohr, Smith, Sz\'ekely, and Whitlatch [Electronic J. Comb. {25}(4) (2018) \#P4.24] observed that the crossing number of any tanglegram is strictly less than $\frac{1}{2}\binom{n}{2}$, but some $n$, some tanglegrams have crossing number at least $\frac{1}{2}\binom{n}{2}-\frac{n^{3/2}-n}{2}$. In the current work we show on the one hand that the crossing number of any tanglegram is at most $\frac{1}{2}\binom{n}{2} -\Omega(n)$, and on the other hand that for some $n$, some tanglegrams have crossing number at least $\frac{1}{2}\binom{n}{2}-O(n\log n)$.
Posted April 2, 2024
Last modified April 3, 2024
LSU AWM Student Chapter LSU AWM Student Chapter Website
11:30 am – 12:30 pm Lockett -Keisler Lounge
Dr. Lisa Kuhn, Southeastern LA University
AWM-Ask me Anything - Dr Lisa Kuhn
This is an informal event where you can ask any questions you might have about her work, career, what it's like to be a woman in math, etc. Food will be provided in the Keisler lounge, and the event will start at 11:30. All are welcome!
Posted March 27, 2024
Last modified April 2, 2024
Dr. Lisa Kuhn, Southeastern LA University
PDE Structures: Finite Elements, Data Science and the Search for Efficient Solutions
Recent advancements in smart materials have significantly influenced the complexity of partial differential equation (PDE) structures, which frequently exhibit material discontinuities and intricate boundary conditions, especially with PDE systems. As we transition further into the age of artificial intelligence, researchers are increasingly exploring machine and deep learning methodologies to derive PDE solutions. However, success has been limited when considering control of distributed parameter systems which is supported by finite element theory. This presentation will present recent findings in generating PDE solutions utilizing both finite elements with adapted bases and hybrid techniques while striving to uphold infinite-dimensional distributed parameter control theory. The discussion will include results of one and two-dimensional clamped structures employing Euler-Bernoulli beams and isotropic plates. Computational methodologies such as modified higher-order bases and neural finite elements will be elaborated upon.
Posted March 28, 2024
Combinatorics Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett Hall 233 (Simulcasted via Zoom)
Eva Czabarka, University of South Carolina
Maximum diameter of $k$-colorable graphs
Between 1965 and 1989 several people showed that the diameter of an $n$-vertex connected graph $G$ with minimum degree $\delta$ is at most $\frac{3n}{\delta+1}-1$. In 1989 Erd\H{o}s, Pach, Pollack and Tuza posed the following conjecture: For fixed integers $r,\delta\geq 2$, for any connected graph $G$ with minimum degree $\delta$ and order $n$ we have (1) If $G$ is $K_{2r}$-free and $\delta$ is a multiple of $(r-1)(3r+2)$ then, as $n\rightarrow \infty$, $$ \operatorname{diam}(G) \leq \frac{2(r-1)(3r+2)}{(2r^2-1)}\cdot \frac{n}{\delta} + O(1)=\left(3-\frac{2}{2r-1}-\frac{1}{(2r-1)(2r^2-1)}\right)\frac{n}{\delta}+O(1). $$ (2) If $G$ is $K_{2r+1}$-free and $\delta$ is a multiple of $3r-1$, then, as $n\rightarrow \infty$, $$\operatorname{diam}(G) \leq \frac{3r-1}{r}\cdot \frac{n}{\delta} + O(1)=\left(3-\frac{2}{2r}\right)\frac{n}{\delta}+O(1). $$ Erd\H{o}s, Pach, Pollack and Tuza also created examples that show that the above conjecture, if true, is tight. Not much progress was made till 2009, when Czabarka, Dankelman and Sz\'ekely showed that for $r=2$ a weaker version of (2) holds: For every connected $4$-colorable graph $G$ of order $n$ and minimum degree $\delta\ge 1$, $ \operatorname{diam}(G) \leq \frac{5n}{2\delta}-1.$ This suggests a weakening of the conjecture by replacing the condition $K_{k+1}$-free with $k$-colorability. With Inne Singgih and L\'aszl\'o A. Sz\'ekely we provided conterexamples of part (1) of the conjecture in both versions (forbidden clique size or colorability) for every $r\ge 2$ for large enough $\delta$. These examples give that, if we are to bound the diameter of a $K_{k+1}$-free $n$-vertex graph with minimum degree $\delta$ by $C_k\cdot\frac{n}{\delta}$, then $C\ge 3-\frac{2}{k}$ regardless of the parity of $k$. With Stephen Smith and L\'aszl\'o A. Sz\'ekely we showed that this modified conjecture holds for both $3$- and $4$-colorable graphs (the latter result is an alternative and shorter proof to the 2009 result).
Posted February 19, 2024
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 232
Jessica Lin, McGill University
TBA
Posted February 21, 2024
Last modified April 8, 2024
Probability Seminar Questions or comments?
3:30 pm
Jessica Lin, McGill University
Generalized Front Propagation for Stochastic Spatial Models
In this talk, I will present a general framework which can be used to analyze the scaling limits of various stochastic spatial "population" models. Such models include ternary Branching Brownian motion subject to majority voting and several examples of interacting particle systems motivated by biology. The approach is based on moment duality and a PDE methodology introduced by Barles and Souganidis, which can be used to study the asymptotic behaviour of rescaled reaction-diffusion equations. In the limit, the models exhibit phase separation with an evolving interface which is governed by a global-in-time, generalized notion of mean-curvature flow. This talk is based on joint work with Thomas Hughes (Bath).
Posted January 18, 2024
Last modified April 5, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Agniva Roy, Louisiana State University
Legendrian Rainbow Closures, Sheaf Moduli, and Grassmanians
Recent advancements in computing invariants of Legendrian knots in the 3-sphere, based on seminal work of Kashiwara-Schapira and continued by Shende- Treumann-Zaslow-Casals-Williams-Gao-Shen-Weng-Hughes-Gorsky-Gorsky-Simental and many others, have uncovered deep connections between contact and symplectic geometry and various properties of algebraic varieties. In this talk, I will try to explore the simplest examples of (k,n) torus links, and show how the sheaf moduli of these links give rise to Grassmanian varieties. Also, we will see how exact Lagrangian fillings give a geometric understanding of Plucker coordinates in the (2,n) case. The talk will focus largely on pictures and examples, with a view towards conveying the fascinating interplay of ideas that happens here.
Posted December 6, 2023
Last modified April 1, 2024
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Joseph Breen, University of Iowa
The Giroux correspondence in arbitrary dimensions
The Giroux correspondence between contact structures and open book decompositions is a cornerstone of 3-dimensional contact topology. While a partial correspondence was previously known in higher dimensions, the underlying technology available at the time was completely different from that of the 3-dimensional theory. In this talk, I will discuss recent joint work with Ko Honda and Yang Huang on extending the statement and technology of the 3-dimensional correspondence to all dimensions.
Posted April 3, 2024
Last modified April 4, 2024
LSU AWM Student Chapter LSU AWM Student Chapter Website
3:30 pm – 4:30 pm Lockett Keisler Lounge
Nadejda Drenska, Louisiana State University
Dr. Nadia Drenska's Journey in Machine Learning.
In this talk, Dr.Nadia Drenska will speak about her journey in machine learning. The talk will consist of both an overview of the area of machine learning and a discussion of various problems. The speaker will focus on two types of problems, originating in `prediction with expert advice’, and in `semi-supervised learning’. The talk is a part of the 2024 AWM workshop on Machine Learning.
Posted April 8, 2024
Combinatorics Seminar Questions or comments?
2:00 pm – 3:00 pm Zoom (Please email zhiyuw at lsu.edu for Zoom link)
Jonathan Tidor, Stanford University
Ramsey and Turán numbers of sparse hypergraphs
The degeneracy of a graph is a measure of sparseness that plays an important role in extremal graph theory. To give one example, a 1966 conjecture of Erdős states that $d$-degenerate bipartite graphs have Turán number $O(n^{2-1/d})$. Though this is still far from solved, the bound $O(n^{2-1/4d})$ was proved by Alon, Krivelevich, and Sudakov in 2003. As another example, the Burr--Erdős conjecture states that graphs of bounded degeneracy have Ramsey number linear in their number of vertices. (This is in contrast to general graphs whose Ramsey number can be as large as exponential in the number of vertices.) This conjecture was resolved by Lee in 2017. I will talk about the hypergraph analogues of these two questions. Though the typical notion of hypergraph degeneracy does not give any information about either the Ramsey or Turán numbers of hypergraphs, I will define a new notion called skeletal degeneracy that is better-suited for these problems. We prove the hypergraph analogue of the Burr--Erdős conjecture: hypergraphs of bounded skeletal degeneracy have Ramsey number linear in their number of vertices. Furthermore, we give good bounds on the Turán number of partite hypergraphs in terms of their skeletal degeneracy. Both of these results use the technique of dependent random choice. Joint work with Jacob Fox, Maya Sankar, Michael Simkin, and Yunkun Zhou.
Posted April 3, 2024
Last modified April 8, 2024
LSU AWM Student Chapter LSU AWM Student Chapter Website
3:30 pm – 3:30 pmMachine Learning Workshop
Join us for an interactive workshop in Machine Learning designed for both Undergraduate and Graduate students. This event is a part of the AWM student chapter event on Machine Learning. Participants can engage in hands-on experience on their computers during the workshop.
Posted January 27, 2024
Last modified March 4, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Sergey Dashkovskiy , Julius-Maximilians-Universität Würzburg
Stability Properties of Dynamical Systems Subjected to Impulsive Actions
We consider several approaches to study stability and instability properties of infinite dimensional impulsive systems. The approaches are of Lyapunov type and provide conditions under which an impulsive system is stable. In particular we will cover the case, when discrete and continuous dynamics are not stable simultaneously. Also we will handle the case when both the flow and jumps are stable, but the overall system is not. We will illustrate these approaches by means of several examples.
Posted March 19, 2024
Computational Mathematics Seminar
until 3:30 pm Digital Media Center 1034
Quoc Tran-Dinh, UNC Chapel Hill
Boosting Convergence Rates for Fixed-Point and Root-Finding Algorithms
Approximating a fixed-point of a nonexpansive operator or a root of a nonlinear equation is a fundamental problem in computational mathematics, which has various applications in different fields. Most classical methods for fixed-point and root-finding problems such as fixed-point or gradient iteration, Halpern's iteration, and extragradient methods have a convergence rate of at most O(1/square root k) on the norm of the residual, where k is the iteration counter. This convergence rate is often obtained via appropriate constant stepsizes. In this talk, we aim at presenting some recent development to boost the theoretical convergence rates of many root-finding algorithms up to O(1/k). We first discuss a connection between the Halpern fixed-point iteration in fixed-point theory and Nesterov's accelerated schemes in convex optimization for solving monotone equations involving a co-coercive operator (or equivalently, fixed-point problems of a nonexpansive operator). We also study such a connection for different recent schemes, including extra anchored gradient method to obtain new algorithms. We show how a faster convergence rate result from one scheme can be transferred to another and vice versa. Next, we discuss various variants of the proposed methods, including randomized block-coordinate algorithms for root-finding problems,which are different from existing randomized coordinate methods in optimization. Finally, we consider the applications of these randomized coordinate schemes to monotone inclusions and finite-sum monotone inclusions. The algorithms for the latter problem can be applied to many applications in federated learning.
Posted January 18, 2024
Last modified April 15, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Krishnendu Kar, Louisiana State University
An Introduction to ‘Spetra’cular category
We define higher homotopy groups of a topological space $X$ by taking homotopy classes of the maps from higher dimensional spheres. These higher-homotopy groups are exponentially more difficult to compute than homology or cohomology groups due to the failure of some robust computational tools such as excision. Excision holds for these groups up to connectivity, and so does the Mayer-Vietoris sequence. The suspension map $\Sigma:X\rightarrow \Sigma X$ induces a map on higher homotopy groups $\Sigma:\pi_n(X)\rightarrow \pi_{n+1}(\Sigma X)$. A theorem by Freudenthal states that after taking enough suspensions, these homotopy groups will stabilize eventually. We call the colimit of these homotopy groups as the stable homotopy group. In the modern treatment of stable homotopy theory, spaces are replaced by spectra. In this talk, we will see some important facts, examples, and, more importantly, justification for the title.
Posted April 1, 2024
Last modified April 15, 2024
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Kevin Schreve, Louisiana State University
Homology growth and aspherical manifolds
Suppose we have a space X and a tower of finite covers that are increasingly better approximations to the universal cover. In this talk, we will be interested in how classical homological invariants grow as we go up the tower. In particular, I will survey various conjectures about the rational/F_p-homology growth and integral torsion growth in these towers. We'll discuss constructions of closed aspherical manifolds that have F_p-homology growth outside of the middle dimension, and give some applications to (non)-fibering of high-dimensional manifolds. This is joint work with Grigori Avramidi and Boris Okun.
Posted April 14, 2024
Combinatorics Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett Hall 233
Xingxing Yu, Georgia Institute of Technology
Planar Turan Number of Cycles
The planar Turan number of a graph $H$, $ex_P(n,H)$, is the maximum number of edges in an $n$-vertex planar graph without $H$ as a subgraph. We discuss recent work on $ex_P(n,H)$, in particular when $H=C_k$ (cycle of length $k$), including our work on $ex_P(n,C_7)$. We prove an upper bound on $ex_P(n, C_k)$ for $k, n\ge 4$, establishing a conjecture of Cranston, Lidicky, Liu, and Shantanam. The discharging method and previous work on circumference of planar graphs are used.
Posted January 6, 2024
Last modified March 4, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Madalena Chaves, Centre Inria d'Université Côte d'Azur
Coupling, Synchronization Dynamics, and Emergent Behavior in a Network of Biological Oscillators
Biological oscillators often involve a complex network of interactions, such as in the case of circadian rhythms or cell cycle. Mathematical modeling and especially model reduction help to understand the main mechanisms behind oscillatory behavior. In this context, we first study a two-gene oscillator using piecewise linear approximations to improve the performance and robustness of the oscillatory dynamics. Next, motivated by the synchronization of biological rhythms in a group of cells in an organ such as the liver, we then study a network of identical oscillators under diffusive coupling, interconnected according to different topologies. The piecewise linear formalism enables us to characterize the emergent dynamics of the network and show that a number of new steady states is generated in the network of oscillators. Finally, given two distinct oscillators mimicking the circadian clock and cell cycle, we analyze their interconnection to study the capacity for mutual period regulation and control between the two reduced oscillators. We are interested in characterizing the coupling parameter range for which the two systems play the roles "controller-follower".
Posted January 28, 2024
Last modified April 1, 2024
Mathematical Physics and Representation Theory Seminar
2:30 pm – 3:20 pm Lockett 233
Greg Parker, Stanford University
$\mathbb Z_2$-harmonic spinors as limiting objects in geometry and topology
$\mathbb Z_2$-harmonic spinors are singular solutions of Dirac-type equations that allow topological twisting around a submanifold of codimension 2. These objects arise as limits at the boundary of various moduli spaces in several distinct areas of low-dimensional topology, gauge/Floer theory, and enumerative geometry. The first part of this talk will introduce these objects, and discuss the various contexts in which they arise and the relationship between them. The second part of the talk will focus on the deformations of $\mathbb Z_2$-harmonic spinors when varying background parameters as a model for the novel analytic problems presented by these objects. In particular, the deformations of the singular submanifold play a role, giving the problem some characteristics similar to a free-boundary-value problem and leading to a hidden elliptic pseudo-differential operator that governs the geometry of the moduli spaces.
Posted April 21, 2024
Probability Seminar Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Ben Seeger, The University of Texas at Austin
Equations on Wasserstein space and applications
The purpose of this talk is to give an overview of recent work involving differential equations posed on spaces of probability measures and their use in analyzing mean field limits of controlled multi-agent systems, which arise in applications coming from macroeconomics, social behavior, and telecommunications. Justifying this continuum description is often nontrivial and is sensitive to the type of stochastic noise influencing the population. We will describe settings for which the convergence to mean field stochastic control problems can be resolved through the analysis of the well-posedness for a certain Hamilton-Jacobi-Bellman equation posed on Wasserstein spaces, and how this well-posedness allows for new convergence results for more general problems, for example, zero-sum stochastic differential games of mean-field type.
Posted February 21, 2024
Last modified April 12, 2024
Applied Analysis Seminar Questions or comments?
3:30 pm Lockett 232
Ben Seeger, The University of Texas at Austin
Equations on Wasserstein space and applications
The purpose of this talk is to give an overview of recent work involving differential equations posed on spaces of probability measures and their use in analyzing mean field limits of controlled multi-agent systems, which arise in applications coming from macroeconomics, social behavior, and telecommunications. Justifying this continuum description is often nontrivial and is sensitive to the type of stochastic noise influencing the population. We will describe settings for which the convergence to mean field stochastic control problems can be resolved through the analysis of the well-posedness for a certain Hamilton-Jacobi-Bellman equation posed on Wasserstein spaces, and how this well-posedness allows for new convergence results for more general problems, for example, zero-sum stochastic differential games of mean-field type.
Posted January 18, 2024
Last modified April 22, 2024
Informal Geometry and Topology Seminar Questions or comments?
1:30 pm Lockett 233, Zoom
Megan Fairchild, Louisiana State University
The Double Branched Cover of the Three-Sphere Over a Knot.
In this talk, we will examine how the double branched cover of the three-sphere over a knot is constructed and the linking form defined on its first homology. We will discuss how to calculate first homology, defining the linking form, and calculating the linking form given a knot diagram. The main goal of the talk is to better understand this object and examine its connection to non-orientable 4-genus of knots.
Posted January 31, 2024
Last modified April 23, 2024
Informal Geometry and Topology Seminar Questions or comments?
3:30 pm Lockett 233
Morgan Weiler, Cornell University
TBA
Posted April 19, 2024
Combinatorics Seminar Questions or comments?
2:00 pm – 3:00 pm Lockett 233
Ryan Martin, Iowa State University
Counting cycles in planar graphs
Basic Tur\'an theory asks how many edges a graph can have, given certain restrictions such as not having a large clique. A more generalized Tur\'an question asks how many copies of a fixed subgraph $H$ the graph can have, given certain restrictions. There has been a great deal of recent interest in the case where the restriction is planarity. In this talk, we will discuss some of the general results in the field, primarily the asymptotic value of ${\bf N}_{\mathcal P}(n,H)$, which denotes the maximum number of copies of $H$ in an $n$-vertex planar graph. In particular, we will focus on the case where $H$ is a cycle. It was determined that ${\bf N}_{\mathcal P}(n,C_{2m})=(n/m)^m+o(n^m)$ for small values of $m$ by Cox and Martin and resolved for all $m$ by Lv, Gy\H{o}ri, He, Salia, Tompkins, and Zhu. The case of $H=C_{2m+1}$ is more difficult and it is conjectured that ${\bf N}_{\mathcal P}(n,C_{2m+1})=2m(n/m)^m+o(n^m)$. We will discuss recent progress on this problem, including verification of the conjecture in the case where $m=3$ and $m=4$ and a lemma which reduces the solution of this problem for any $m$ to a so-called ``maximum likelihood'' problem. The maximum likelihood problem is, in and of itself, an interesting question in random graph theory. This is joint work with Emily Heath and Chris (Cox) Wells.
Posted January 17, 2024
Last modified March 4, 2024
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Tobias Breiten, Technical University of Berlin
On the Approximability of Koopman-Based Operator Lyapunov Equations
Computing the Lyapunov function of a system plays a crucial role in optimal feedback control, for example when the policy iteration is used. This talk will focus on the Lyapunov function of a nonlinear autonomous finite-dimensional dynamical system which will be rewritten as an infinite-dimensional linear system using the Koopman operator. Since this infinite-dimensional system has the structure of a weak-* continuous semigroup in a specially weighted Lp-space one can establish a connection between the solution of an operator Lyapunov equation and the desired Lyapunov function. It will be shown that the solution to this operator equation attains a rapid eigenvalue decay, which justifies finite rank approximations with numerical methods. The usefulness for numerical computations will also be demonstrated with two short examples. This is joint work with Bernhard Höveler (TU Berlin).
Posted February 1, 2024
Last modified April 30, 2024
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Jean-François Lafont, The Ohio State University
Strict hyperbolizations produce linear groups
Strict hyperbolization is a process developed by Charney--Davis, which inputs a simplicial complex, and outputs a negatively curved piecewise hyperbolic space. By applying this process to interesting triangulations of manifolds, one can create negatively curved manifolds with various types of pathological large scale behavior. I will give a gentle introduction to strict hyperbolization, and will explain why the fundamental groups of the resulting spaces are always linear over Z. This is joint work with Lorenzo Ruffoni (Tufts University).
Posted April 16, 2024
Last modified April 29, 2024
Faculty Meeting Questions or comments?
3:00 pm – 4:00 pm Lockett 232Meeting with Dean Cynthia Peterson