Posts

Autumn 2025 – Spring 2026 Seminars

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Seminar Time: Tuesdays 11:30-12:30

Location: Math Tower MW 154

August 26:

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September 2:

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September 9:

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September 16: Anna Ghazaryan (Miami University, Ohio)

Title: Regime dependent infection propagation fronts in a epidemiological model
Abstract: We consider a diffusive version of an S-I-S (Susceptible-Infected-Susceptible) epidemiological model which includes a saturating incidence in the size of the susceptible population. We seek traveling fronts in this model in the following regimes: when both susceptible and infected populations move around at comparable rates; when the infection slows the population down; when the infected population diffuses faster than the susceptible population. In all three regimes we show that traveling fronts exist. In the latter regime we derive a bound for the speeds of propagation of the infection. We also identify a regime when the spread of the disease is governed by the Burgers-FKPP equation. The paper uses applied dynamical system techniques and geometric singular perturbation theory. This is a joint work with Dr. Vahagn Manukian and  two students, Jonathan Waldmanna and Priscilla Yinzime.

September 23:

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September 30:

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October 7:

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October 14:

Avner Friedman (Ohio State University)

Title: Mathematical modeling of osteoarthritis and its treatment
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Osteoarthritis is a disease of the joint, with the knee as the most common location. The disease is a progressive destruction of the cartilage between the two adjoining bones, it causes increasing levels of pain, and in severe cases it requires knee replacement. 33 million Americans are affected annually, with 1.5 women than men.
OA increases with age, typically starting to become noticable after age.50 The disease cannot be cured, and currently there are only few clinical trials that aim to slow its progress.
In this talk I will explain the biological background of the course of the disease and present a mathematical model of OA by a system of PDEs The model will then be used to demonstrate how a combination of two specific drugs can effectively slow the disease progression, especially if treatment starts early.
This is a joint recent work with Nourridine Siewe from RIT.

October 21:

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October 28:

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November 4: Stephen Anco (Brock University)

Title: Peakon equations
Abstract:Peakons are peaked travelling waves which arise as solutions of the integrable Camassa-Holm equation in water wave theory discovered 30 years ago. In the explosion of work on peakons following that discovery, several basic questions have been asked about the nature of peakons — What is the most general class of nonlinear dispersive wave equations possessing peakon solutions? Is integrability necessary for existence of multi-peakon solutions? Are peakons best understood as weak solutions or distributional solutions? Does the NLS equation have a peakon counterpart? How to find integrable peakon equations systematically? In this talk, I will review my contributions to understanding and attempting to answer these questions over the past decade, which have led to some unexpected and on-going new developments.

November 11: Adrian Lam (Ohio State)

Title: Hamilton-Jacobi Approach in Wave Propagation Problems
Abstract: I will discuss the speed and more generally the shape of expansion in wave propagation problems. The key idea is to exploit the passage to the limiting Hamilton-Jacobi equation, whose solution can be characterized by the principle of least action (or geometric optics). Examples of such applications include the Fisher-KPP equations in heterogeneous media or ones that subject to a shifting climate. We also discuss the spatial spread of a population in two-dimensional domain where diffusion is fast on the x-axis.

November 14: Helena Lopes (The Federal University of Rio de Janeiro)

          Title: Beyond the resolution of the Onsager Conjecture
          Abstract: In a seminal 1949 paper Lars Onsager conjectured, using dimensional analysis, that it might be possible for some incompressible inviscid flows not to conserve energy, as long as they were sufficiently rough. This is in line with the Kolmogorov 1941 theory of turbulence. More precisely, Onsager conjectured that, if a solution of the Euler equations were more regular than Holder continuous with exponent 1/3 then energy would be conserved; otherwise energy might not be balanced. Research on the Onsager Conjecture developed intensely in the early 2000s, following DeLellis and Sezekelyhidi’s introduction of the use of convex integration to fluid dynamics. The Conjecture was fully resolved by Isett in 2018 but there are still many issues to be understood. In this talk I will give a brief account of the resolution of the Onsager Conjecture and then concentrate on ongoing subsequent research, particularly regarding two dimensional flows. I aim to discuss recent results for vanishing viscosity solutions in the supercritical case.

November 14: Milton Lopes (The Federal University of Rio de Janeiro)

          Title: Nonseparable mean field games in spaces of pseudomeasures
          Abstract: Mean field games can be modeled by a system of PDE of the form $u_t + H(t,x,Du,m) = -\Delta u$ and $m_t + div(m H_p(t,x,Du,m) = \Delta m$, with initial data $m(0,x) = m_0(x)$ and a terminal condition of the form $u(T,x) = G(m(T,x),x)$. The nonlinearity $H$ is the Hamiltonian and $H_p$ is the gradient of $H$ with respect to the $Du$ variable.  The $G$ is called the payoff, and it is a nonlocal operator.  The variable $m$ represents a distribution of “agents” and $u$ is an action function. Separable Hamiltonians are those of the form $H_1(.,m) + H_2(.,Du)$ and most of the results known in this context apply to separable, convex nonlinearities. However, there are interesting applications for which these structural hypothesis do not apply. The results we will present apply to nonlocal, nonseparable Hamiltonians of the form $H = g(Du) \int f(du) m dx$, which are relevant for certain models of resource extraction and a model for management of household wealth.

Under appropriate conditions on the Hamiltonian and the payoff, we prove well-posedness of this problem on the d-dimensional torus for $m_0$ in the space of pseudomeasures, i.e., measures whose Fourier coefficients are globally bounded. In addition, we prove that the solution depends continuously on the initial measure $m_0$ in the weak-star topology of the space of bounded measures. This is relevant since mean field games model the limiting behavior of games with a finite number of agents, which the weak-star topology on initial data captures in a more natural way than the stronger topology of pseudomeasures

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November 21: Sam Krupa (École normale supérieure in Paris, France)

Title: Are $L^\infty$ solutions to hyperbolic systems of conservation laws unique?
Abstract: For hyperbolic systems of conservation laws in 1-D, fundamental questions about uniqueness and blow up of weak solutions still remain even for the apparently “simple” systems of two conserved quantities such as isentropic Euler and the p-system. Similarly, in the multi-dimensional case, a longstanding open question has been the uniqueness of weak solutions with initial data corresponding to the compressible vortex sheet. We address all of these questions by using the lens of convex integration, a general method of constructing highly irregular and non-unique solutions to PDEs. Our proofs involve computer-assistance. This talk is based on joint work with László Székelyhidi, Jr.

November 25:

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December 9:

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Jan 9 (special seminar): Kesh Govinder (University of KwaZulu-Natal)

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Feb 26:

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Apr 7: Cole Graham (University of Wisconsin–Madison)

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