Mathematics Colloquium Series

Mathematics Department Colloquium Series 

The Mathematics Department established the Mathematics Department Colloquium Series through a Faculty Development Grant in 1999 to provide a place to discuss new research in Mathematics. Speakers for the series come from both inside the UTC Department of Mathematics as well as guest speakers from other institutions. The Colloquium Series meets periodically throughout the year.

Upcoming Colloquium Talks

Mohandas Pillai

  • Date/Time: Fri., Sept. 18 at 3:30 p.m.
  • Location: Lupton 393
  • Title: Near soliton dynamics for the critical, two-equivariant Schrodinger map problem
  • Abstract: I will talk about work in progress with Ioan Bejenaru (UCSD), Daniel Tataru (UC Berkeley) regarding the critical, 2-equivariant Schrödinger map problem into the two-sphere. I will start with a result we proved in 2024, regarding the global existence of topological degree 2 solutions with energy close to that of the ground state solitons, along with a stability result for a more regular set of initial data. This motivates the question of the existence of infinite time relaxation in addition to infinite time singularity forming solutions. I will speak about work in progress regarding those questions.

Brian Choi

  • Date/Time: Fri., Sept. 25 at 3:30 p.m.
  • Location: Lupton 393
  • Title: Long-time continuum limits for twisted Schrodinger lattices
  • Abstract: This talk explores the long-time justification of Hamiltonian PDEs from a numerical analysis perspective, guided by complete integrability. Focusing on the discrete nonlinear Schrödinger equation with a phase twist, we synthesize Birkhoff coordinates and modified energies to establish polynomial-in-time bounds for the nonlinear approximation error, effectively bypassing the limitations of the Grönwall inequality.

Thien Le

  • Date/Time: Fri., Oct. 2 at 3:30 p.m.
  • Location: Lupton 393
  • Title: Coming Soon
  • Abstract: High-resolution temporal network data provide an increasingly detailed picture of how interactions change over time. Yet translating this wealth of information into reliable models of spreading processes remains challenging. We investigate this challenge using empirical contact networks from diverse real-world settings and compare spreading processes across different temporal resolutions. Our results show that hourly resolution often produces dynamics comparable to finer-resolution data, while daily observations can substantially distort spreading behavior. These findings provide practical guidance on collecting dynamic network data to study spreading processes.

Ayca Cetinkaya

  • Date/Time: Fri., Oct. 23 at 3:30 p.m.
  • Location: Lupton 393
  • Title: Building bridges between differential equations: The idea of transmutation
  • Abstract: In this work, we study a family of transformation operators for a specific differential operator with an integrable potential. We establish the existence of the transmutation kernel by using the method of successive approximations. We derive explicit integral representations for these operators on specified function spaces and analyze their properties.

Jin Wang

  • Date/Time: Fri., Oct. 30 at 3:30 p.m.
  • Location: Lupton 393
  • Title: Fluid-structure interaction: Modeling, simulation, and applications
  • Abstract: The interaction between fluid flows and immersed solid structures leads to nonlinear multi-physics phenomena that have applications to a wide range of scientific and engineering disciplines. There are many numerical techniques currently available for computing fluid-structure interaction, but we will focus on methods of the immersed boundary type in this presentation. Starting from the original immersed boundary method, we will discuss a few improvements of the method as well as their applications. Following that, we will describe an extension of this computational approach to deal with immersed structures that occupy a nonzero volume and that satisfy detailed constitutive laws. We will illustrate the application of these methods through several numerical examples.

Will Erickson

  • Date/Time: Fri., Nov. 13 at 3:30 p.m.
  • Location: Lupton 393
  • Title: Random shuffles with a fixed shape
  • Abstract: A shuffle is a rearrangement of the integers 1,...,n, and its "shape" is a partition of n which measures the longest unions of increasing subsequences. This notion of "shape," as a global statistic on shuffles, is nearly 100 years old, and is a linchpin of modern algebraic combinatorics; before this year, however, the local effect of shape on shuffles had not yet been studied. That is, for a random shuffle with some fixed shape, what is the probability that the number i occupies position j? In this talk, we share our solution to this problem for three families of shapes ("hooks," "two-row," and "rectangles"), focusing on the surprising visual patterns revealed by the probability formulas. The main souvenir of the talk will be a glimpse of the remarkable RSK correspondence (where the "K" is Donald Knuth), which is the key tool in our technique. The audience should also be prepared for the unexpected appearance of a famous integral from Calculus II. We conclude with several open questions, some of which would make good research problems for interested undergraduates

TBD

  • Date/Time: Coming Soon
  • Location: Lupton 393
  • Title: Coming Soon
  • Abstract: Coming Soon

Mathematics

Mathematics