Graduate Seminar

Current contact: Thomas Ng and Geoffrey Schneider.

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.

• Thursday September 6, 2012 at 15:30, Wachman 617

  Graduate Student pizza party and social!

   

• Thursday September 20, 2012 at 15:30, Wachman 617

  Total curvature of knots and curves. 

  Matt Evans, Temple University

• Thursday October 4, 2012 at 15:30, Wachman 617

  Braid groups and public key cryptology.

  Christian Millichap, Temple University

• Thursday October 18, 2012 at 15:30, Wachman 617

  Compressive sensing and radar imaging. 

  Michael Minner, Drexel University

• Thursday November 1, 2012 at 15:30, Wachman 617

  Lp

• spectra of certain singular integral operators. 

  Eric Stachura, Temple University

• Thursday November 15, 2012 at 15:30, Wachman 617

  Borsuk-Ulam and combinatorics. 

  Arran Hamm, Rutgers University

• Thursday December 6, 2012 at 15:30, Wachman 617

  Graph theoretic preconditioners and linear matrix equations

  Steve Shank, Temple University

Current contact: Thomas Ng and Geoffrey Schneider.

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.

• Thursday February 7, 2013 at 15:30, Wachman 617

  May's recognition principle for iterated loops spaces.

  Brian Paljug, Temple University

• Thursday February 21, 2013 at 15:30, Wachman 617

  An introduction to Gelfand-Kirillov dimension

  Jessie Hamm, Temple University

• Thursday March 7, 2013 at 15:30, Wachman 617

  Quantum mechanics without the mechanics. 

  Matt Lagro, Temple University

• Thursday March 21, 2013 at 15:30, Wachman 617

  "Maschke's Theorem" for Hopf algebras.

  Matt Evans, Temple University

Current contact: Thomas Ng and Geoffrey Schneider.

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.

• Friday January 24, 2014 at 14:30, Wachman 617

  Algebras of smooth functions

  Geoffrey Schneider, Temple University

• Friday January 31, 2014 at 14:30, Wachman 617

  The Reflector Problem and the Inverse Square Law. 

  Ahmad Sabra, Temple University

• Friday February 7, 2014 at 14:30, Wachman 617

  Graduate student panel. 

Current contact: Thomas Ng and Geoffrey Schneider.

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.

• Friday January 30, 2015 at 14:30, Wachman 617

  (Co)sheaves and applications

  Geoff Schneider, Temple University

• Friday February 6, 2015 at 14:30, Wachman 617

  Homotopy probability theory

  Brian Paljug, Temple University

• Friday February 13, 2015 at 15:00, Wachman 617

  A gentle introduction to Fuchsian groups

  -Note different time-

  Tim Morris, Temple University

Current contact: Thomas Ng and Geoffrey Schneider.

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.

• Friday January 15, 2016 at 14:30, Wachman 617

  General Meeting

  -Note different time-

• Friday January 22, 2016 at 14:30, Wachman 617

  Acylindrically Hyperbolic Groups

  -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.

   

• Friday January 29, 2016 at 13:30, Wachman 617

  Mednykh's Formula

  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.

   

• Friday February 5, 2016 at 13:30, Wachman 617

  Spectral Properties of the Hardy Kernel Operators and Application to Second Order Elliptic Boundary Value Problems 

  Hussein Awala, Temple University

   

  In this talk I will present an old result of David Boyd from the 70's regarding the Lp

spectrum of Mellin convolution type singular integral operators, 1<p<∞

• , 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.

   

   

• Friday February 12, 2016 at 13:30, Wachman 617

  Magical things that happen when you combine a quadrature rule, a Krylov subspace, and a matrix function 

  Kathryn Lund-Nguyen, Temple University

• Friday February 19, 2016 at 13:30, Wachman 617

  Reciprocity Laws and Conjectures

  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.

   

• Friday March 11, 2016 at 13:30, Wachman 617

  Local and global well-posedness for the H1(Rn)

• subcritical Nonlinear Schrodinger

  Serena Federico, MIT and Universita di Bologna

   

• Friday March 25, 2016 at 13:30, Wachman 617

  Perturbation Formulas for Gross-Pitaevskii Equation with Periodic Potential 

  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.

   

• Friday April 1, 2016 at 13:30, Wachman 617

  Game theory for dummies

  Farhan Abedin, Temple University

• Friday April 8, 2016 at 13:30, Wachman 617

  Quasiconvex Hierarchies for Relatively Hyperbolic Non-Positively Curved Cube Complexes 

  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.

   

• Friday April 15, 2016 at 13:30, Wachman 617

  Manifolds, representations and varieties Oh my!

  Timothy Morris, Temple University

• Friday April 22, 2016 at 13:30, Wachman 617

  The adjoint representation for Hopf algebras

  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.

   

• Friday September 9, 2016 at 13:30, Wachman 617

  Graph Complexes

  Geoffrey Schneider, Temple University

• Friday September 16, 2016 at 13:30, Wachman 617

  Standard 2-complexes for group presentations

  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.

   

• Friday September 23, 2016 at 13:30, Wachman 617

  Tate's thesis

  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.

   

• Friday October 7, 2016 at 13:30, Wachman 617

  Angle structures and ideal triangulations

  William Worden, Temple University

• Friday October 14, 2016 at 13:30, Wachman 617

  The Analyst's Traveling Salesman Theorem

  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.

   

• Friday October 28, 2016 at 13:30, Wachman 617

  An introduction to (arithmetic) lattices

  Nick Miller, Purdue University

• Friday November 4, 2016 at 13:30, Wachman 617

  The Magical World of Mapping Class Groups

  Jacob Russell, CUNY Graduate center

• Friday December 2, 2016 at 13:30, Wachman 617

  TBA

  Michael Maillloux, Temple University

  TBA

Current contact: Thomas Ng and Zachary Cline.

The seminar takes place on Fridays (from 1:00-2:00pm) in Room 617 on the sixth floor of Wachman Hall. Pizza and refreshments are available beforehand in the lounge next door.

• Friday February 3, 2017 at 13:00, Wachman 617

  Introduction to Deformation Theory

  Elif Altinay-Ozaslan, Temple University

• Friday February 10, 2017 at 13:00, Wachman 617

  Studying fundamental groups through representation theory

  Timothy Morris, Temple University

• Friday February 17, 2017 at 13:00, Wachman 617

  Growth of groups: an introduction to geometric group theory

  Thomas Ng, Temple University

• Friday March 10, 2017 at 13:00, Wachman 617

  What are Hopf algebras and why should you care? 

  Zachary Cline, Temple University

• Friday March 24, 2017 at 13:00, Wachman 617

  TBA

  Adam Jacoby, Temple University

• Friday April 21, 2017 at 13:00, Wachman 617

  TBA

  Kathryn Lund, Temple University

• Friday September 15, 2017 at 13:00, Wachman 617

  The complex of curves of a surface

  Thomas Ng, Temple University

  We will explore the definition and properties of this object and its role in studying 2 and 3 dimensional topology. With some luck we will see the definition of a simplicial complex, hear a little about the mapping class group (the group of homeomorphisms of a surface... sorta), or stumble across a unicorn or two (provided we are punctured).

• Friday September 29, 2017 at 13:00, Wachman 617

  Representations from roots of the Alexander polynomial

  Timothy Morris, Temple University

• Friday October 13, 2017 at 13:00, Wachman 617

  Partitions of equiangular tight frames

  James Rosado, Temple University

  Presentation on a new efficient algorithm to construct partitions of a special class of equiangular tight frames (ETFs) that satisfy the operator norm bound established by a theorem of Marcus, Spielman, and Srivastava (MSS), which they proved as a corollary yields a positive solution to the Kadison–Singer problem.

• Friday October 20, 2017 at 13:00, Wachman 617

  Introduction to Operads

  Tai-Danae Bradley, CUNY Graduate Center

  Operads are, loosely speaking, gadgets that encode various flavors of algebras: associative, commutative, Lie, A-infinity, etc., and they have a wide range of applications: deformation theory, algebraic topology, and mathematical physics, to name a few. While the formal definition of an operad may look daunting, we’ll see that it is really quite intuitive. To begin, we’ll have a brief discussion of symmetric monodical categories (which are needed to define operads) and then proceed to define and look at examples of operads.

• Friday October 27, 2017 at 13:00, Wachman 617

  2 is an algebra!: a bit of abstract nonsense

  Zachary Cline, Temple University

• Friday November 10, 2017 at 13:00, Rm 617

  Construction of solutions of a functional system of ODEs with applications to bichromatic lens design

  Ahmad Sabra, University of Warsaw

  In this talk we will consider the following system of ODE

  $$Z'(t) = H(t; Z(t), Z(z_1(t)), Z'(t), Z'(z_1(t))), \qquad Z(0) = 0$$ with $Z=(z_1, \dots, z_n) \in \mathbb{R}^n$ and $H(\mathbb{R}^{4n+1} \to \mathbb{R}^n)$ a given Lipschitz continuous function. We show using a fixed point argument that under some conditions on $H$ the system has a unique local solution. We use this result to construct lenses that refract bichromatic rays (2 colors) emitted from a point source into a parallel beam.

   

with Z=(z1,…,zn)∈Rn and H(R4n+1→Rn) a given Lipschitz continuous function. We show using a fixed point argument that under some conditions on H the system has a unique local solution. We use this result to construct lenses that refract bichromatic rays (2 colors) emitted from a point source into a parallel beam.

Current contact: Rebekah Palmer and Timothy Morris

The seminar takes place on Fridays (from 2:30-3:30pm) in Room 617 on the sixth floor of Wachman Hall. Pizza and refreshments are available beforehand in the lounge next door.

• Friday February 2, 2018 at 11:00, Rm 617

  Jones polynomial as a quantum invariant

  Zachary Cline, Temple University

  There is a cool construction of a variant of this polynomial which is instructive and which anyone remotely interested in knot theory should see at least once in their life. I will present this construction and then explain how this polynomial invariant arises as a functor from the tangle category to the category of vector spaces over C

• .

• Friday February 9, 2018 at 11:00, Rm 617

  Random graphs and surfaces

  Thomas Ng, Temple University

  We will describe a model introduced by Bollob\'as for random finite k-regular graph. In the case when k=3, we will discuss connections with two constructions of random Riemann surfaces introduced by Buser and Brooks-Makover. Along the way, we will see a glimpse of the space of metrics on a surface (Teichmuller space) and (ideal) triangulations.

• Friday February 16, 2018 at 16:00, Rm 617

  Numerical linear algebra: the hidden math in everything

  Kathryn Lund, Temple University

• Friday February 16, 2018 at 16:30, Rm 617

  Building blocks for low-dimensional manifolds

  Thomas Ng, Temple University

• Friday March 16, 2018 at 11:00, Rm 617

  Eigenvalues of analytic kernels

  Narek Hovsepyan, Temple University

  It is shown that the eigenvalues of an analytic kernel on a finite interval go to zero at least as fast as $R^{ - n} $ for some fixed $R < 1$.

• . The best possible value of R is related to the domain of analyticity of the kernel. The method is to apply the Weyl–Courant minimax principle to the tail of the Chebyshev expansion for the kernel. An example involving Legendre polynomials is given for which R is critical.

  Reference - G. Little, J. B. Reade, Eigenvalues of analytic kernels , SIAM J. Math. Anal., 15(1), 1984, 133–136.

• Friday March 23, 2018 at 11:00, Rm 617

  The tree for SL(2)

  Khanh Le, Temple University

• Friday March 30, 2018 at 11:00, Rm 617

  A gentle foray into quaternion algebras

  Rebekah Palmer, Temple University

  In 1843, Hamilton carved "$i^2=j^2=k^2=ijk=-1$"

into a bridge in Dublin after a spark of inspiration while on a walk. His original intention was to make the complex numbers C more complex (it worked). The restriction to −1

• has since then been loosened in favor of generalization, known as quaternion algebras. We'll explore some introductory facts and see how these constructions occur in geometry.

• Friday April 13, 2018 at 11:00, Rm 617

  TBA

  Geoff Schneider

• Friday April 20, 2018 at 11:00, Rm 617

  Introduction to the generalized law of reflection/refraction

  Luca Pallucchini, Temple University

• Friday April 27, 2018 at 11:00, Rm 617

  Incompressible surfaces in 4-punctured sphere bundles

  Sunny Yang Xiao, Brown University

• Friday August 31, 2018 at 13:30, Wachman 617

  Welcome back and info seminar

  We will be doing introductions for the new grad students, have a small presentation from TUGSA, playing board games, and eating pizza!

• Friday September 7, 2018 at 14:30, Wachman 617

  Conway's ZIP proof of the Classification of Surfaces

  Tim Morris, Temple University

  We present John Conway's proof of the classification of surfaces. This proof, is considered by many to capture the essence an simplicity of purely topological arguments. So, naturally we will include many pictures to help aid our intuition. This talk will be accessible for all graduate students.

• Friday September 14, 2018 at 14:30, Wachman 617

  Mathematical Modeling of Biofilm in Marble Environment

  Yilin Wu, Temple University

  Bacterial biofilms are defined as clusters of bacterial cells living in the self-produced extracellular polymeric substances (EPS), and always attached to various kinds of surfaces, such as tissues, solid surfaces, or cells. Biofilms can be formed of a population that developed from a single species or a community derived from multiple microbial species. I will give a brief introduction to the biofilm living environment on marble with a mathematical approach.

   

• Friday September 21, 2018 at 14:30, Wachman 617

  Interpolation, Recovery, and Extrapolation

  Narek Hosyepyan, Temple University

  We will discuss some interpolation formulae, such as Pick interpolation, recovery formulae for analytic functions from pieces of their boundary or interior data, and some aspects of the question of their extrapolation.

• Friday October 5, 2018 at 14:30, Wachman 617

  Quantum Symmetries

  Zach Cline, Temple University

• Friday October 12, 2018 at 14:30, Wachman 617

  Classifying Group Elements by their Dynamics on Boundaries

  Thomas Ng, Temple University

  One incredibly fruitful means of understand an infinite group is to realize it as a subgroup of an isometry group of some unbounded metric space. In the setting of fundamental groups of Riemann manifolds, this metric space can be taken to be the universal cover. Not all group elements are created equal. Some elements may have finite order any others may have cyclic centralizers. We will study geometric characteristics of the action of each group element to see that much of this information can be We will consider a few foundational examples from topology to guide us in a tour through various notions of boundary for unbounded metric spaces and try to understand in which settings each is most useful.

• Friday October 19, 2018 at 14:30, Wachman 617

  Mathematical and Molecular Modeling of Flow-Sensitive Biopolymers

  Michael Morabito, Lehigh University

  von Willebrand Factor (vWF) is a large multimeric protein found in blood plasma. vWF plays an indispensable role in the blood clotting process by initiation of clot formation that stops bleeding due to vascular damage. vWF is able to sense elevated hydrodynamic force in blood flow at the site of vessel hemorrhage, and respond by undergoing conformational changes. Understanding the functionality of this flow-sensitive biological polymer requires interdisciplinary collaboration. The dynamics and mechanical response behavior of vWF can be probed using coarse-grained Brownian molecular dynamics simulations. The mathematical foundations of this method will be presented, and simulation results for vWF in shearing flows will be discussed. Simulation and experimental results are also used as input to machine learning algorithms, which have proven to be powerful data-driven analysis tools for this bioinformatics application.

• Friday October 26, 2018 at 14:30, Wachman 617

  A flavor of complex dynamics

  Tantrik Mukerji, Temple University

  This will be a light-hearted survey of complex dynamics where we'll touch on some relevant objects of study within the field. This talk will be intuitive and interactive with demonstrations.

• Friday November 2, 2018 at 14:30, Wachman 617

  An Introduction to Geometric Structures

  Khánh Lê, Temple University

  Manifolds arise in nature and in mathematics in many different ways. Fairly frequently, they come equipped with some special patterns. In this talk, we will present different constructions of manifolds. We will then discuss how certain patterns of manifolds can be used as building blocks for different structures.

• Friday November 9, 2018 at 14:30, Wachman 617

  No Seminar

  NA Day, learn about Numerical Analysis!

• Friday November 16, 2018 at 14:30, Wachman 617

  Title TBA

  James Rosado, Temple University

• Friday November 30, 2018 at 14:30, Wachman 617

  Title TBA

  Ben Stucky, University of Oklahoma

• Friday December 7, 2018 at 14:30, Wachman 617

  Title TBA

  Luca Pallucchini, Temple University

Current contact: Brandi Henry and Rebekah Palmer

The seminar takes place on Fridays at 1:00 pm in Room 617 on the sixth floor of Wachman Hall. Pizza and refreshments are available beforehand in the lounge next door.

• Friday February 1, 2019 at 14:30, Wachman Hall 617

  Cannon's conjecture

  Thomas Ng, Temple University

  Abstract: The class of all groups (even finitely generated ones) are known to have wildly inefficient, in fact often unsolvable, algorithmic properties. It is thus helpful to specialize to well-behaved subclasses. In the early 1900s Dehn studied groups as geometric objects and showed that finitely generated groups arising as the fundamental group of manifolds in dimensions less that 4 are often very algorithmically efficient. Given the existence of these well-behaved groups, one is naturally led to ask how unique they are or under what conditions are they uniquely determined. Following Gromov's notion of boundary for a hyperbolic group introduced in 1987, Cannon conjectured that for hyperbolic groups the condition that its boundary is a 2-sphere uniquely determines 3-manifold fundamental groups. In this talk we will briefly review the notions of Cayley graph, hyperbolicity, and boundary of a group. We will then survey some of the recent results that inspired and attempt to solve the Cannon conjecture.

• Friday February 8, 2019 at 14:30, Wachman Hall 617

  Resolution of singularities

  Rebekah Palmer, Temple University

  Abstract: To study structures that are not quite smooth, it is convenient to transform them so that we can apply the many tools developed for smooth structures. Given a variety with singularities, we ask if there is a consistent method of transformation into a non-singular variety. In this talk, we will introduce ourselves to some varieties with singularities, demonstrate how to uniquely resolve algebraic curves, and further discuss approaches to resolving higher-dimensional varieties.

   

• Friday February 15, 2019 at 14:30, Wachman Hall 617

  Bead Movement in Biofilms: Effects of Curli Amyloids and Analysis of Density Dependence

  Brandi Henry, Temple University

  Abstract: Microbial cells form communities, called biofilms, by producing an extracellular adhesive. By tracking the movement of 1µm glyoxylate beads in biofilms through the use of laser-scanning confocal microscopy and image-processing software, we can study the properties of the biofilm that may affect interactions of other cells with the microbiota. We developed a tool that can analyze the distance the beads travel, the volume of the region within which the beads travel, the time for which the bead is associated with the biofilm, the velocity with which the bead travels, and density of the region within which the bead travelled. Bead movement was studied for Enterococcus faecalis, Salmonella Typhimurium, Escherichia coli biofilms, and their isogenic curli mutants. Consistent with visual observations, our statistical analysis showed that the presence of curli in biofilms introduces a rigidity to the biofilm structure. Conversely, the lack thereof correlates to more bead movement suggesting less rigidity. In biofilms lacking curli where more free movement occurred, we analyzed the dependency of bead movement on the local density. While greater movement occurred in less dense environments, bead movement is not strictly dependent on density, suggesting other material properties of the biofilm influence bead movement.

• Friday February 22, 2019 at 14:30, Wachman Hall 617

  Classifying Actions of Tn⊗Tn

on Path Algebras of Quivers

Delaney Aydel, Temple University

Abstract:

Let $T_n$ denote the $n$th Taft algebra. We fully classify inner-faithful actions of $T_n \otimes T_n$ on four-vertex Schurian quivers as extensions of the actions of $\mathbb{Z}_n \times \mathbb{Z}_n$. One example will be presented in full, with the remaining results briefly given.

•  

• Friday March 29, 2019 at 14:30, Wachman Hall 617

  New off-ramp coupling conditions on the road

  Najmej Salehi, Temple University

• Friday April 19, 2019 at 14:30, Wachman Hall 617

  The Class Number One Problem

  Dong Bin Choi, Temple University

  Abstract:

In 1952, Kurt Heegner proved (up to minor gaps) that the imaginary quadratic fields $K$ with class number $h(K) = 1$ are $\mathbb{Q}(\sqrt{d}$ with $d = -1, -2, -3, -7, -11, -19, -43, -67, -163$. To understand the problem in context, we begin from integer quadratic forms $Q(x,y) = ax^2 + bxy + cy^2$ and the question of what numbers $n$ occur as solutions to $ax^2 + bxy + cy^2 = n$ for a given $a, b, c$. This depends on the equivalence class of the quadratic form, which turns out to be closely related to ideal classes of the quadratic integer ring with discriminant $b^2 - 4ac$. We touch on some number-theoretic notions used in Heegner's proof, such as the genus of a quadratic form and the $j$-invariant of lattices. We sketch Heegner's proof (following Kezuka 2012), and conclude with solutions to some generalizations of the problem.

• Friday September 6, 2019 at 13:00, Wachman Hall 617

  Welcome Back

   

• Friday September 13, 2019 at 13:00, Wachman Hall 617

  Explicit power laws in analytic continuation problems via reproducing kernel Hilbert spaces.

  Narek Hovsepyan, Temple University

  Abstract: The need for analytic continuation arises frequently in the context of inverse problems. We consider several such problems and show that they exhibit a power law precision deterioration as one moves away from the source of data. We introduce a general Hilbert space-based approach for determining these exponents. The method identifies the "worst case" function as a solution of a linear integral equation of Fredholm type. In special geometries, such as the circular annulus, an ellipse or an upper half-plane the solution of the integral equation and the corresponding exponent can be found explicitly.

  This is a joint work with Yury Grabovsky

• Friday September 27, 2019 at 13:00, Wachman Hall 617

  Groups Acting on Trees

  Rylee Lyman, Tufts University

  Abstract: We introduce the Bass–Serre theory of groups acting on trees. Two common constructions on groups are the amalgamated free product and HNN extension. We begin by reviewing these constructions. Bass–Serre theory generalizes these constructions within the common framework of an action of the group on a tree. When the group is finitely generated, examining the quotient yields a presentation for the group, as well as other algebraic information. We describe the notion of the fundamental group of a graph of groups, a useful tool in the study of finitely generated groups, and, time permitting, famous theorems of Stallings and Dunwoody.

• Friday October 4, 2019 at 13:00, Wachman Hall 617

  Modeling an Action Potential and Neuronal Behavior

  James Rosado, Temple University

  Abstract: In this talk we explore the Hodgkin-Huxley conductance-based model which is used to describe the initiation and propagation of an action potential. We will also explore the different levels of modeling neuronal behavior and interactions: how is an action potential initiated within a neuron, how does an action potential induce communication between neurons, how do we model the interactions of neuronal networks? We will also present the current research that is being done to model intracellular behavior of a neuron.

• Friday October 11, 2019 at 13:00, Wachman Hall 617

  Extension of groups

  Khanh Le, Temple University

  Abstract: In this talk, we will introduce the concept of an extension of groups. Roughly speaking, given two groups G

and K what are the different ways to write down a short exact sequence 1→K→E→G→1

• ? To understand this question, we will naturally introduce the idea of group cohomology. After that, we explore different examples of extensions of groups.

• Friday October 18, 2019 at 13:00, Wachman Hall 617

  Some invariant metrics under biholomorphic maps

  Elie Abdo, Temple University

  Abstract: Several theorems that hold in the theory of one complex variable cannot be generalized to the theory of several complex variables, one of them is the Riemann Mapping Theorem. In fact, invariant metrics are important tools that can be used to show that the open bi-disc and the open unit-ball in C2

• are not biholomorphic. In this talk, we introduce some invariant metrics, the Kobayashi, Caratheodory and Sibony metrics, list some of their properties, and do some interesting examples.

• Friday October 25, 2019 at 13:00, Wachman Hall 617

  Weyl's Law: From Isometries to Eigenvalues

  Lindsay Dever, Bryn Mawr College

  Abstract: Complex-valued, square-integrable functions on compact, hyperbolic 3-manifolds decompose uniquely into special functions called automorphic forms. These special functions are eigenfunctions of the Laplacian operator which are invariant under a discrete group of isometries. In general, it is a hard problem to determine the eigenvalues explicitly, but we do know how many eigenvalues to expect asymptotically. The asymptotic formula for the number of eigenvalues is known as Weyl's law. The proof of Weyl's law involves the Selberg trace formula, which connects these eigenvalues to geometric information about the manifold. In this expository talk, I will introduce hyperbolic 3-manifolds, define automorphic forms, and give a proof of Weyl's law for compact, hyperbolic 3-manifolds.

• Friday November 1, 2019 at 13:00, Wachman Hall 617

  Optimal Finite Volume Limiter Functions

  Abhijit Biswas, Temple University

  Abstract: Hyperbolic conservation law has discontinuous solutions, even if the initial condition is smooth. We want to have schemes that are both accurate in smooth regions and non-oscillatory near discontinuities or sharp transition. Typical finite volume linear schemes can not fulfill those two desired properties simultaneously, even for linear advection problems. One way to get those two desired properties is to use limiter functions with a high order accurate linear scheme, for example, the Lax-Wendroff method. Many limiter functions have been introduced in the literature, and the general approach is to design a limiter function and demonstrate that it performs well on some test problems. Here we wish to investigate the inverse problem instead: given a portfolio of representative test cases, and a cost functional, determine the optimal limiter function.

• Friday November 8, 2019 at 13:00, Wachman Hall, 617

  The adjoint action of group algebras

  Ramy Yammine, Temple University

  Abstract: In this talk we discuss the adjoint action of a group algebra k[G] on itself. We focus primarily on the ¨finite part¨ of this action, a group-subalgebra of k[G] that is better behaved. We will then discuss some interesting problems and questions about k[G] that reduce to its finite part.

Current contact: Brandi Henry and Ruth Meadow-MacLeod

The seminar takes place on Fridays from 3:00 to 4:00pm on Zoom, and there will be a social time from 2:00 to 3:00pm in lieu of the refreshments usually offered.

• Friday January 17, 2020 at 12:00, Wachman 617

  Welcome back

   

• Friday January 24, 2020 at 13:00, Wachman 617

  Triangle groups and their behavior on surfaces

  Rebekah Palmer, Temple University

  Abstract: The tessellation of surfaces is an ongoing question. A healthy place to start is with a class of relatively uncomplicated tiles — triangles! We construct the triangle groups geometrically by reflecting triangles across their three edges and propagating. From here, we can express the group as an algebraic structure. We will explore what properties can be deduced about these groups in both geometric and algebraic contexts as well as the grander implications of how we approach tiling surfaces.

• Friday January 31, 2020 at 13:00, Wachman 617

  Dr. Joan Birman and the Jones Polynomial

  Katherine Burke, Temple University
  
  Abstract: Come one, come all, and learn about the pros and cons of the Jones polynomial as an invariant of a closed 3-braid link.  Based Birman’s ‘85 On the Jones Polynomial of Closed 3 Braids.

• Friday February 7, 2020 at 13:00, Wachman 617

  Graduating Grad Student Panel

  A panel of soon-to-graduate grad students will describe their experiences and give their advice on how to approach the penultimate and the last years of the PhD program at Temple, including the required paperwork, the job market, and the dissertation process.

• Friday February 14, 2020 at 13:00, Wachman 617

  Techniques for parameter sensitivity analysis of mathematical modeling

  Zhi Li, Temple University

  Abstract: Understanding the significance and sensitivity of parameters plays an important role in mathematical modeling. A sensitivity analysis of the parameters is not only critical to model validation but also serves to guide future research efforts. We will talk about several of the more practical methods for conducting parameter sensitivity studies, ranging from one-at-a-time sensitivity measures to standardized regression coefficients to statistical tests.

• Friday February 21, 2020 at 13:00, Wachman 617

  The Mathematics of Gerrymandering

  Rose Kaplan-Kelly, Temple University

  Abstract: Based on the work of Moon Duchin.

• Friday March 13, 2020 at 13:00, Wachman 617

  Asynchronous algorithms

  Xinli Yu, Temple University

  Abstract: With the advent of parallel computers, many new algorithms were devised or rediscovered for the new architectures. Asynchronous parallel solvers are new techniques that speed up thecomputation time. The main character of asynchronous algorithm is that the local algorithms donot have to wait at predetermined points for predetermined messages to become available. Asynchronous method has wide applications. In this talk applications of asynchronous iterations todifferent areas will be discussed.

• Friday March 27, 2020 at 13:00, Wachman 617

  Najmeh Salehi, Temple University

   

• Friday April 3, 2020 at 13:00, Wachman 617

  Chia-Han Chou, Temple University

   

• Friday April 10, 2020 at 13:00, Wachman 617

  Thomas Ng, Temple University

   

• Friday April 17, 2020 at 13:00, Wachman 617

  Alexander Ahn, Temple University

   

• Friday September 11, 2020 at 15:00,

  Left Ordering of Group

  Khanh Le, Temple University

  Abstract: In this talk, we will discuss left ordering of a group. We will focus on basic examples of groups which admit a left order and properties of the space of left orders. If time permits, we discuss some interesting questions and connections of left ordering on groups to 3-manifold topology.

Current contact: Brandi Henry and Ruth Meadow-MacLeod

The seminar takes place on Fridays from 3:00 to 4:00pm on Zoom, and there will be a social time from 2:00 to 3:00pm in lieu of the refreshments usually offered.

• Friday January 22, 2021 at 15:00,

  Advanced Canvas Workshop

  
  For the first graduate seminar of the semester, we thought it would be helpful to run an advanced Canvas workshop. Our very own Delaney Aydel will begin the workshop by demonstrating: 
   

  • how to organize your Canvas site & make your Canvas site navigable without sacrificing aesthetics
  • how to implement mastery paths
  • how to use the "Commons" to share materials across courses
  • surveys on Canvas
  • various features within Canvas quizzes
  • how to access analytics.

  
  We hope to also have discussions on good resources for students and how to best encourage our students to engage with them, on using the discussion board feature in a math course, and on how to utilize active learning in virtual education. We also invite and encourage questions, other discussion topics, and any other useful demonstrations or tips! 

   

• Friday January 29, 2021 at 15:00,

  Quaternion Algebras in Geometry

  Rebekah Palmer, Temple University

  Abstract: Quaternion algebras are a generalization of Hamilton's quaternions which are applied in the mechanics of three-dimensional space. These algebras provide a firm link between number theory and geometry. In this talk, we'll discuss how to construct these algebras, to associate them with matrices, and to harness their structure to make strong conclusions about hyperbolic 2- and 3-manifolds.

• Friday February 5, 2021 at 15:00,

  Macroscopic Interpretation of Microscopic Models with Traffic Waves

  Nour Khoudari, Temple University
  
  Abstract: Real traffic flow develops instabilities and traffic waves. Traffic waves are traveling disturbances in the distribution of vehicles on a highway. They travel backwards relative to the vehicles themselves. Low density autonomous vehicles, acting as Lagrangian flow actuators, have the potential to dampen and prevent these undesirable non-equilibrium phenomena. By connecting traffic models from micro to macro scales, we outline some of the key macroscopic flow consequences of microscopic traffic waves and AV-based flow smoothing.

• Friday February 12, 2021 at 15:00,

  The Mapping Class Group and the k-Curve Graph

  Rob Oakley, Temple University

  Abstract: One of the most common ways to understand a group is to understand how it acts on spaces. The mapping class group is no different! In this talk I hope to illustrate one 'flavor' of space that the mapping class group acts on rather nicely. I will focus on a specific example, the k-curve graph to explore the mapping class group action on it.

• Friday February 19, 2021 at 15:00,

  Navier-Stokes equations in 3D

  Elie Abdo, Temple University
  
  Abstract: The Navier-Stokes (NS) equations are partial differential equations describing the flow of incompressible fluids. It has been shown that global smooth solutions exist in the two-dimensional case. In this talk, we study the NS equations in three-dimensional bounded smooth domains: we prove existence of global weak solutions and unique local strong solutions. 

• Friday February 26, 2021 at 15:00,

  Longest Common Subsequences

  Apo Demirelli, Temple University

  Abstract: The theory of longest common subsequences is one of the most well-studied problems of probability theory. It has lots of applications from computer science to computational biology. In recent years, this problem has become more popular than ever with the improvements on the gene matchings and the similarity problems. In this talk, we will investigate some properties of the longest common subsequences in random words, examine upper and lower bounds for the expected value of the longest common subsequences in this setting, and discuss the behavior of the asymptotic order of the longest common subsequences’s variance. We will also study the relationship between longest common subsequences and longest increasing subsequences in random permutations and discuss some properties of the matrix L(n) that is generated by the length of the longest common subsequences of permutations.

• Friday March 5, 2021 at 15:00,

   

  Brandi Henry, Temple University

  Abstract: Biofilms are communities of microorganisms that form when these microorganisms attach to surfaces, secrete a sticky substance, and reproduce within this sticky extracellular matrix. Biofilms enable interactions between the microorganisms, such as the exchange of genetic material. We are interested in how the structure of the biofilms within the human gastrointestinal tract affects these interactions, and specifically how structural changes relate to antibiotic resistance. Structural changes can occur when biofilms are stressed. Hydrogen peroxide is one such stressor that causes rigid, dense towers to grow within the biofilm, resulting in a highly heterogeneous structure. We will discuss our recent work in reconstructing the biofilm environments from microscopy data and modeling and simulating movement of antibiotics through the biofilm environments when put under flow.

• Friday April 9, 2021 at 15:00,

  Random Walks on Weakly Hyperbolic Groups

  Leah Leiner, Temple University

  Abstract: Let G be a countable group of isometries acting on a Gromov hyperbolic space. Then G is called weakly hyperbolic if it contains a pair of independent hyperbolic isometries— one wide studied example of such a group is the mapping class group acting on its curve complex. In this talk, we will discuss random walks on these groups, and show they almost surely converge to the Gromov boundary.

• Friday April 16, 2021 at 15:00,

  Links in Thickened Surfaces

  Rosie Kaplan-Kelly, Temple University

  Abstract:

A link is alternating if it has a diagram with an orientation such that, if we travel along the link according to this orientation, we will alternate between over- and under-crossings. Traditionally, alternating links have been studied with alternating diagrams on $S^2$ in $S^3$. In this talk we will consider links which are alternating on higher genus surfaces in $S_g \times I$. We will sketch Howie and Purcell's theorem giving conditions for when such links are hyperbolic. We will then define what it means for the complements of these generalized alternating links to be right-angled and discuss work towards proving which links will have this property.

• . We will sketch Howie and Purcell's theorem giving conditions for when such links are hyperbolic. We will then define what it means for the complements of these generalized alternating links to be right-angled and discuss work towards proving which links will have this property.

• Friday April 23, 2021 at 13:00,

  Transshipment Problem, its conversion into a transportation problem and its applications

  Irem Altiner, Temple University

  Abstract: Transshipment problem involves sending products from sources/warehouses to the determined destinations/sinks via some middle centers we call transshipment points. Using these transshipment points may reduce the total cost of transportation significantly. In this talk we will talk about how we treat this problem as a transportation problem and we will talk about a couple of its numerous applications including Brazilian soybean exportation based on real needs and statistics and vaccine distribution, if time allows.

Current contact: Irem Altiner and Ross Griebenow -MacLeod

The seminar takes place on Fridays from 1:00 to 2:00pm on the sixth floor of Wachman Hall, and pizza and refreshments are available beforehand (from 12:00 to 1:00pm) in the lounge next door.

• Friday October 7, 2022 at 13:30,

  Singular integral operators of layer potential type and boundary value problems

  Artur Henrique de Oliveira Andrade

  Abstract TBA

• Friday November 4, 2022 at 13:00,

  Approximation of solutions to the incompressible Navier-Stokes equations via incompressible Euler equations

  Lancelot Leung

  In this talk, we will give some simple exact solutions to the incompressible Euler/Navier-Stokes equations. Then, we use those simple exact solutions to illustrate how to approximate the solution of the incompressible Navier-Stokes equations via the incompressible Euler equations. After that, we will discuss how we use energy estimates to prove a similar result to the smooth solutions to both equations.

Current contact: Irem Altiner and Ross Griebenow -MacLeod

The seminar takes place on Fridays from 1:00 to 2:00pm on the sixth floor of Wachman Hall, and pizza and refreshments are available beforehand (from 12:00 to 1:00pm) in the lounge next door.

• Friday March 31, 2023 at 13:00,

  The Birch and Swinnerton-Dyer Conjecture - A Millennial Problem

  Aniruddha Sudarshan

  In this talk, we look at one of the Clay millennial problems in Mathematics: the BSD conjecture. It connects an algebraic aspect of an elliptic curve with a complex analytic aspect of the L-function of an elliptic curve. We cover some basics of elliptic curves, their group law, and L-functions attached to them. In the end, we talk about some qualitative (probabilistic) results on the elliptic curves for which that BSD conjecture holds. This talk will be as self contained as possible.