The talk is devoted to the study of traveling waves for a semilinear parabolic equation, the nonlinear term of which can have both a local and a non-local character. This is primarily the equation considered in the seminal work of Kolmogorov, Petrovskii and Piskunov. We consider a class of nonlinearities that arise in connection with the development of applications in voting models based on branching Brownian motion. We present an analytical solution that generalizes the results of Ablowitz and Kaliappan to a broader class of equations. The method of constructing exact solutions also applies to the nonlocal modification of the KPP equation that arises from population dynamics.

The talk will be streamed through “Kontur Talk”: https://mian.ktalk.ru/xr9pf6k3br12?pinCode=2494

We study the derivation of the spatially homogeneous Landau equation from the mean-field limit of a conservative $N$-particle system, obtained by passing to the grazing limit on Kac's walk in his program for the Boltzmann equation. Our result covers the full range of interaction potentials, including the physically important Coulomb case. This provides the first resolution of propagation of chaos for a many-particle system approximating the Landau equation with Coulomb interactions, and the first extension of Kac's program to the Landau equation in the soft potential regime. The convergence is established in weak, Wasserstein, and entropic senses, together with strong $L^1$ convergence. For the Maxwellian molecule case, we also derive a quantitative convergence in relative entropy from the Nanbu particle system. In my talk, which is based on https://arxiv.org/abs/2511.05478, I will try to give an introduction to the subject and state some of my recent results.

The talk will be streamed through "Tencent": https://meeting.tencent.com/dm/vy8Nw2So88u9. meeting code: 349-700-913 To join via a web browser: go to https://voovmeeting.com/; click "Log in" in the upper-right corner and login either by a Google/Apple account, or by a verification code received on phone or email; click "Join now" in the upper-right corner and type the number of the meeting 349-700-913 in the "Enter meeting ID" field; when prompted, select "Join from browser".