Group and Galois cohomology is an important tool that gets used in many areas of mathematics. We will have a learning seminar on this topic this semester. During this meeting we will explain a bit of the motivation for choosing this topic and assign topics for future talks. If you are interested in giving a talk this semester, please attend this meeting!
This week we'll have a talk by Aniruddha Sudarshan on the Prime Number Theorem and its connection to the Riemann zeta function. And, of course, there will be free pizza!
Abstract: In the talk, we will look at the prime number theorem, and its connection to the Riemann zeta function. If we have time, we dwell into the notion of density of primes. This talk doesn’t assume any prior knowledge of higher math
Numerical Linear Algebra II
3
In person
MW 10:30-11:50
The film is "an award-winning documentary that investigates the biggest crises of our time—political polarization, racial and economic inequity, a global pandemic, and climate change—through an unexpected lens: math. In our current information economy, math is everywhere. The people we date, the news we see, the influence of our votes, the candidates who win elections, the education we have access to, the jobs we get—all of it is underwritten by an invisible layer of math that few of us understand, or even notice."
The capacity for tomorrow's screening is 100, so if you plan to attend, please register in advance. This is the registration link with the trailer: https://www.eventbrite.com/e/temple-university-libraries-counted-out-film-screening-tickets-1080435354229
Artur Andrade, Temple University
Abstract: Elliptic boundary value problems arise naturally in modeling a wide range of physical phenomena, including electrostatics, elasticity, steady-state incompressible fluid flow, and electromagnetism. A powerful tool for the treatment of such problems is the layer potential method, through which matters are reduced to solving a boundary integral equation involving a singular integral operator naturally associated with the domain, and a coefficient tensor for the underlying PDE. When this singular integral operator is compact, the boundary integral equation can be treated using Fredholm Theory. While systematic progress has been made in the study of second-order elliptic systems along these lines, the case of higher-order elliptic systems remains far less understood.
In this talk, I will present a distinguished coefficient tensor for the polyharmonic operator $\Delta^3$ in all dimensions, and illustrate how the associated singular integral operator is compact on $L^p$ Lebesgue-type spaces, for all integrability exponents $p\in(1,\infty)$, thus opening the door for the employment of Fredholm Theory for the solvability of the Dirichlet Problem for $\Delta^3$ in infinitesimally flat AR domains.
This is an ongoing work with Dorina Mitrea (Baylor University), Irina Mitrea (Temple University), and Marius Mitrea (Baylor University).
Junzhi Huang (Yale University)
In 3-dimension topology, the study of foliations, flows and fundamental group actions on 1-manifolds are closely related. Given a closed 3-manifold, one can construct a fundamental group action on a circle from either a taut foliation or a pseudo-Anosov flow in the manifold by different works of Thurston, Calegari-Dunfield and Fenley. When the foliation is depth-one and the pseudo-Anosov flow is transverse to the foliation, we show (with some extra assumptions) that the circle actions from both settings are topologically conjugate. Moreover, the two circles admit extra structures that are compatible in a natural sense.
Ellis Buckminster, University of Pennsylvania
Abstract: Endperiodic maps are a class of homeomorphisms of infinite-type surfaces whose compactified mapping tori have a natural depth-one foliation. By work of Landry-Minsky-Taylor, every atoroidal endperiodic map is homotopic to a type of map called a spun pseudo-Anosov. Spun pseudo-Anosovs share certain dynamical features with the more familiar pseudo-Anosov maps on finite-type surfaces. A theorem of Thurston states that pseudo-Anosovs minimize the number of periodic points of any given period among all maps in their homotopy class. We prove a similar result for spun pseudo-Anosovs, strengthening a result of Landry-Minsky-Taylor.
Join us for a talk by Professor Seibold on traffice waves, vehicle automation, and traffic modeling. And, of course, there will be free pizza!
Abstract: Traffice often forms waves, including phantom jams, caused by the collective behavior of drivers. These patterns, though frustrating, reveal fascinating dynamics akin to detonation waves. This talk explores how mathematical models and real-world experiments show that even a few automated vehicles can make traffic smoother, safer, and more energy-efficient, reshaping the future of mobility.
Thomas Koberda, University of Virginia
Abstract: It is a difficult and deep problem to understand countable groups that can act by homeomorphisms on compact manifolds, especially in dimension two or more. I will discuss some new ways of investigating groups acting on manifolds through ideas from mathematical logic. This talk will include work that is joint with Sang-hyun Kim and J. De la Nuez Gonzalez.
Olivia Chu, Bryn Mawr College
Abstract: Evolutionary dynamics shape social and biological systems across scales, from the evolution of multicellularity to the emergence of underground fungal symbioses to the formation and maintenance of animal groups and human societies. In these complex adaptive systems, small-scale interactions and associations can lead to emergent, large-scale phenomena. These interactions are often greatly influenced by various forms of heterogeneity, such as personality differences in human populations and variation in altruistic tendencies in animals. In this talk, I will present several models of complex social and biological systems, motivated by real-world phenomena and observations. These models are driven by evolutionary game theory, opinion dynamics frameworks, and agent-based modeling, and employ tools from stochastic processes, differential equations, and dynamical network analysis. I will discuss applications such as the evolution of cooperation, social group formation, the effects of environmental shocks on political opinions and activism, and altruistic tensions in social insect populations.