Colloquium Archives for Academic Year 2022

Cycles on products of elliptic curves and a conjecture of Bloch-Kato

When: Wed, December 1, 2021 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Wei Zhang (MIT) -

Abstract: One classical way to study rational or integral solutions of apolynomial equation is to look at the simpler questions of the various
congruence equations modulo n for all integers n. The conjecture of
Birch and Swinnerton-Dyer predicts that, for elliptic curves (defined by
equations of the form y^2=x^3+ax+b with integer coefficients), the data
from these congruence equations mod n should actually encode much
information on the solutions in rational numbers. In the first talk we
will discuss a generalization of the question to the product of several
elliptic curves, where, instead of rational points, we look for
algebraic cycles (i.e., parameter solutions) modulo suitable equivalence
relations (rational equivalence, Abel—Jacobi or its p-adic version). In
particular, I'll report some recent results on a conjecture of Bloch-Kato.

Entropy and random walks in materials, biology and quantum information science (AWM Colloquium)

When: Wed, December 8, 2021 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Maria Emelianenko (GMU) -
Abstract: What does mathematics, materials science, biology and quantum information science have in common? It turns out, there are many connections worth exploring. I this talk, I will focus on graphs and entropy, starting from the classical mathematical constructs and moving on to applications. We will see how the notions of graph entropy and KL divergence appear in the context of characterizing polycrystalline material microstructures and predicting their performance under mechanical deformation, while also allowing to measure adaptation in cancer networks and entanglement of quantum states. We will discover unified conditions under which master equations for classical random walks exhibit nonlocal and non-diffusive behavior and discuss how quantum walks may allow to realize the coveted exponential speedup.

Mathematical assessment of vaccination against the COVID-19 pandemic in the United States

When: Tue, February 1, 2022 - 3:15pm
Where: BRB 1103

Speaker: Abba Gumel (Arizona State University)
Abstract: The coronavirus that emerged out of Wuhan city in 2019 (COVID-19) became the greatest public health challenge humans have faced since the 1918 influenza pandemic. As of early January 2022, the pandemic (caused by SARS-CoV-2) accounts for over 310 million confirmed cases and 5.5 million fatalities globally. Control and mitigation efforts against the disease were largely based on the use of nonpharmaceutical interventions (NPIs), such as quarantine, isolation, social-distancing, face mask usage, lockdowns etc., until safe and effective vaccines were given emergency use authorization (EUA) by the United States Food and Drug Administration (FDA) at the end of 2020 and during early 2021. In this talk, I will present mathematical models for assessing the impact of the widespread vaccination program (using any of the three FDA-EUA vaccines) on curtailing the spread of the COVID-19 pandemic in the United States. Conditions for achieving vaccine-derived herd immunity (needed for the elimination of the pandemic) in the presence or absence of a variant of concern will be derived. The impact of combining the vaccination program with other NPIs, such as the use of face masks (of varying effectiveness) in public, will also be assessed.

Mathematics of malaria transmission dynamics: the renewed quest for eradication

When: Wed, February 2, 2022 - 3:15pm
Where: Kirwan Hall 3206

Speaker: Abba Gumel (Arizona State University)
Abstract: Malaria, a deadly disease caused by protozoan Plasmodium parasites, is spread between humans via the bite of infected adult female Anopheles mosquitoes. Over 2.5 billion people live in geographies whose local epidemiology permits transmission of P. falciparum, responsible for most of the life-threatening form of malaria. The disease causes over 400,000 deaths globally each year, with most of the deaths occurring in children under the age of five. Since about the year 2000, numerous important global efforts have been embarked upon aimed at malaria eradication. These efforts resulted in a dramatic reduction of malaria incidence and mortality in endemic areas. Although multiple factors, such as early diagnosis, improved drug therapy and better public health infrastructure, have contributed to such success, the major reason for the extraordinary success is believed to be the large-scale and heavy use of insecticide-based interventions, particularly long-lasting insecticidal nets (LLINs) and indoor residual spraying (IRS), to target the mosquito population. Unfortunately, such heavy use of insecticides has also resulted in widespread Anopheles resistance to all the active ingredients used in LLINs and IRS. Another factor that may pose major challenge to the eradication effort is climate change (since the lifecycles of the malaria mosquito and parasites are greatly affected by changes in local climatic conditions). This presentation is based on using a genetic-epidemiology modeling framework to assess the combined impact of insecticide resistance and climate change on malaria transmission in endemic settings. We will explore the feasibility of achieving the eradication objective using the currently-available mosquito control resources (i.e., LLINs and IRS). The potential effectiveness of some of the alternative biological (gene editing) methods being proposed to suppress the malaria mosquito population, such as the release of sterile male mosquitoes into the wild, will also be discussed.

Department Meeting

When: Wed, February 16, 2022 - 3:15pm

Department Meeting

When: Wed, February 23, 2022 - 4:00pm

Geometries of topological groups

When: Wed, March 2, 2022 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Christian Rosendal (UMD) -
Abstract: We will discuss how topological groups (of which Banach spaces are a particular example) come equipped with inherent geometries at both the large and small scale. In the context of Banach spaces, the ensuing study is part of geometric nonlinear analysis and we shall present various results and fundamental concepts dealing both with Banach spaces and more general topological groups appearing in analysis, dynamics and topology.

Non-local games and graphs

When: Wed, April 6, 2022 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Samuel Harris (TAMU) -
Abstract: Non-local games originated in the 1960s as experiments that can demonstrate behaviors in quantum mechanics that cannot be replicated using classical mechanics alone. Since that time, these games have received considerable attention, partially due to the deep connections between them and other areas of mathematics, such as non-commutative geometry, functional analysis, combinatorics and computational complexity theory. In this talk, we will look at examples of non-local games that relate to graph theory, such as the coloring game, the homomorphism game, and the isomorphism game for graphs. We will see recent progress on these games towards separating some of the common models used in quantum information. We will also look at some of the major open problems in this area.

Counterexamples for generalizations of the Schrödinger maximal operator (AWM Colloquium)

When: Wed, April 20, 2022 - 3:15pm
Where: Online by Zoom
Speaker: Lillian Pierce (Duke University) -
Abstract: In 1980 Carleson posed a question: how “well-behaved” must an initial data function be, to guarantee pointwise convergence of the solution of the linear Schrödinger equation? After progress by many authors, this was recently resolved (up to the endpoint) by a combination of two celebrated results: one by Bourgain, whose counterexample construction for the Schrödinger maximal operator proved a necessary condition, and a complementary result of Du and Zhang, who proved a sufficient condition. In this talk we describe a study of Bourgain’s counterexamples, from first principles. Then we describe a new flexible number-theoretic method for constructing counterexamples, which opens the door to studying convergence questions for many more dispersive PDE’s. Along the way we’ll see why no mathematics we learn is ever wasted, and how the boundary from one mathematical area to another is not always clear.

Existence and regularity of anisotropic minimal surfaces

When: Wed, April 27, 2022 - 3:15pm
Where: Kirwan Hall 1311
Speaker: Antonio De Rosa (UMD) -
Abstract: In the first part of the talk I will focus on the existence of anisotropic minimal surfaces, presenting our existence result of nontrivial closed surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth 3-dimensional Riemannian manifolds. In particular, we solve a conjecture of Allard (Invent. Math., 1983) in dimension 3. In the second part of the talk, I will focus on the regularity of anisotropic minimal surfaces, showing our $C^{1,\alpha}$-regularity theorem for m-dimensional Lipschitz graphs with anisotropic mean curvature bounded in $L^p$, $p>m$, in every dimension and codimension.

The Simplicity Conjecture

When: Wed, May 4, 2022 - 3:15pm
Where: Kirwan Hall 3206
Speaker: Daniel Cristofaro-Gardiner (UMD) -
Abstract: In the 60s and 70s, there was a flurry of activity concerning the question of whether or not various subgroups of homeomorphism groups of manifolds are simple, with beautiful contributions by Kirby, Mather, Fathi, Thurston, and many others. A funnily stubborn case that remained open was the case of area-preserving homeomorphisms of surfaces. For example, for balls of dimension at least 3, the relevant group was shown to be simple by work of Fathi from the 1970s, but the answer in the two-dimensional case was not known.   My talk will be about some recent joint work solving many of the mysteries of the two-dimensional case; in particular, we resolved the “Simplicity conjecture”, which stated that the group of area-preserving homeomorphisms of the two-disc that are the identity near the boundary is not simple.  My talk will be to explain some of how this works.  No prior knowledge of symplectic geometry will be assumed.