2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019
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.
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 $C$.
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.
Kathryn Lund, Temple University
Thomas Ng, Temple University
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.
Khanh Le, Temple University
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.
Geoff Schneider
Luca Pallucchini, Temple University
Sunny Yang Xiao, Brown University
We will be doing introductions for the new grad students, have a small presentation from TUGSA, playing board games, and eating pizza!
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.
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.
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.
Zach Cline, Temple University
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.
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.
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.
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.
NA Day, learn about Numerical Analysis!
James Rosado, Temple University
Ben Stucky, University of Oklahoma
Luca Pallucchini, Temple University