The seminar takes place on Fridays (from 1:30-2:30pm) in Room 617 on the sixth floor of Wachman Hall. Pizza and refreshments are available beforehand in the lounge next door.
-Note different time-
-Note different time-
Carolyn Abbott, University of Wisconsin-Madison
Acylindrically hyperbolic groups, a generalization of hyperbolic groups, are groups that have a particular kind of action on a hyperbolic metric space. Recently defined, this class of groups is broad enough to include many groups of interest, including mapping class groups and fundamental groups of many 3-manifolds, while still maintaining a robust theory leading to many new and interesting results. We will define acylindrically hyperbolic groups, give (lots of) examples, and survey some main results in the field.
Kevin Donoghue, UC Berkeley
There are some well-known invariants in 3-dimensional topology that involve representations of Lie groups. This is confusing to the topologist, who don't know when representation theory entered into topology. This talk will be about a beautiful analogous formula from 2-dimensional topology that answers the question of where the representation theory comes from. I will review all the representation theory needed.
Hussein Awala, Temple University
In this talk I will present an old result of David Boyd from the 70's regarding the \(L^p\) spectrum of Mellin convolution type singular integral operators, \(1 < p < \infty\), and then I will discuss its relevance to establishing well-posedness results for second order elliptic boundary value problems in polygonal domains in two dimensions.
Kathryn Lund-Nguyen, Temple University
Edmund Karasiewicz, Rutgers University
One aspect of the Langlands Program, known as the Langlands Reciprocity Conjecture, deals with a relationship between geometric objects, such as solutions of systems of polynomial equations, and analytic objects, such as Hecke characters and modular forms. We will begin with a discussion of quadratic reciprocity and then transition into examples of reciprocity laws involving elliptic curves and modular forms.
Serena Federico, MIT and Universita di Bologna
Seonguk Kim, University of Alabama at Birmingham
In this talk, we investigate the perturbation formulas for Gross-Pitaevskii Equations (GPE) with periodic potential, which is relevant to study Bose-Einstein condensate loaded into optical lattices. In the first part of this study we consider the perturbation formulas for Linear Schroedinger equation with periodic potential. In the second part, we use the results of the perturbation formulas of the linear equation to find a stationary solution and its corresponding value for GPE. Here, we need several methods such as: perturbation theory, spectral theory and successive method.
Farhan Abedin, Temple University
Teddy Einstein, Cornell University
Non-positively curved (NPC) cube complexes are important tools in low dimensional topology and group theory and play a prominent role in Agol's proof of the Virtual Haken Conjecture. Constructing a hierarchy for a NPC cube complex is a powerful method of decomposing its fundamental group essential to the theory of NPC cube complex theory. When a cube complex admits a hierarchy with nice properties, it becomes possible to use the hierarchy structure to make inductive arguments. I will explain what a quasiconvex hierarchy of an NPC cube complex is and briefly discuss some of the applications. We will see an outline of how to construct a quasiconvex hierarchy for a relatively hyperbolic NPC cube complex and some of the hyperbolic and relatively hyperbolic geometric tools used to ensure the hierarchy is indeed quasiconvex.
Timothy Morris, Temple University
Adam Jacoby, Temple University
The talk will prove some know results on the adjoint representation of a finite groups and Lie algebras and discuses partial generalizations to more general classes of Hopf algebras.
Geoffrey Schneider, Temple University
Thomas Ng, Temple University
For a chosen group presentation we can associate a standard 2-dimensional topological object that encodes group theoretical properties in geometric and topological characteristics. This point of view has been incredibly fruitful in the modern study of groups and can be thought of as the birth place of geometric group theory. We will give a short introduction of fundamental groups and covering spaces of a topological space before discussing growth of a group and angle structures: tools have been used in the seminal work of Gromov drawing strong connections between group theory and CAT(0) geometry.
Dianbin Bao, Temple University
In this talk, I will start with Riemann's proof of the functional equation of the Riemann zeta function using poisson summation formula and then introduce the modern point of view of the functional equation from Tate's thesis.
William Worden, Temple University
Silvia Ghinassi, Stony Brook University
Peter Jones, in 1990, found a characterization of subsets of rectifiable curves in the plane. This characterization is given in terms of a multiscale sum of \beta-numbers. Those numbers measure, in a quantitative way, how much a given set fails to be a line. In later years, Okikiolu, David and Semmes, among many, generalized and extended the result. We'll discuss the main definitions and ideas behind the result, together with an overview of the extensions and generalizations up to this day. If time permits, we will briefly discuss some applications in geometric measure theory and harmonic analysis.
Nick Miller, Purdue University
Jacob Russell, CUNY Graduate center
Michael Maillloux, Temple University