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 $\mathbb{C}$ 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