Date: 29 April 2026
Venue: Gewu Building，Room315
9:00-9:40 Benoît Perthame (SU)
Title: Mathematical models of living tissues and free boundary problem
abstract: Tissue growth, as it occurs during solid tumors development, can be described at a number of different scales from the cell to the organ. For a large number of cells, multicomponent 'fluid mechanical' approaches have been advocated in mathematics, biomechanics or biophysics.
We will give an overview of the modeling aspects and of the links between those mathematical models. Then, we will focus on the compressible model describing the cell population density based on systems of porous medium type equations with reaction terms. A more macroscopic 'incompressible' description is based on a free boundary problem close to the classical Hele-Shaw equation. In the stiff pressure limit, one can derive a weak formulation of the corresponding Hele-Shaw free boundary problem and one can make the connection with its geometric form.
The mathematical tools related to these questions include multi-scale analysis, a priori estimate, and emergence of instabilities.
9:50-10:30 Xudong Lai (HIT)
Title: Weak (1,1) estimates for maximal truncated rough singular integral operators
Abstract: In their seminal work (Amer. J. Math. 1956), Calderón and Zygmund introduced the maximal truncated rough singular integral operator and established its Lp-boundedness for 1 < p<∞. However, the endpoint case p = 1 remained an open problem. In this talk, we show our recent result which resolves this problem. More precisely, we prove that the maximal truncated rough singular integral operator is of weak type (1,1).
10:30-10:50 Break（中场休息）
10:50-11:30 Fabrice Bethuel (SU)
Title: Agrregation phenomena in branched transportation
Abstract: Branched transportation is an optimal transportation theory in which the density of transportation decreases the cost, so that branch points might by favored. It offers a convincing example of fractal sets. Its description involves an exponent $\upalpha$: many results in branched transportation are constrained by the fact that the exponent is supercritical, that is larger than the value $\displaystyle{\upalpha_m=1-\frac{1}{m}}$. I will discuss several properties of the branching process which are valid also in the critical and sub-critical cases, the latter raising new challenges.
12:00-14:00 Lunch Break（午餐休息）
14:40-15:20 Emmanuel Trélat (SU)
Title: On the turnpike property
Abstract: The turnpike property was discovered in the 50’s by the Nobel Prize Samuelson in econometry. It stipulates that the optimal trajectory of an optimal control problem in large time remains essentially close to a steady state, itself being the optimal solution of an associated static optimal control problem.
We have established the turnpike property for general nonlinear finite and infinite dimensional optimal control problems, showing that the optimal trajectory is, except at the beginning and the end of the time interval, exponentially close to some (optimal) stationary state, and that this property holds as well for the optimal control and for the adjoint vector coming from the Pontryagin maximum principle. We prove that the exponential turnpike property is due to an hyperbolicity phenomenon which is intrinsic to the symplectic feature of the extremal equations. We infer a simple and efficient numerical method to compute optimal trajectories in that framework, in particular an appropriate variant of the shooting method.
The turnpike property turns out to be ubiquitous and the turnpike set may be more general than a single steady-state, like for instance a periodic trajectory. We also show the property of shape turnpike for PDE models in which a subdomain evolves in time according to some optimization criterion.
These works are in collaboration with Gontran Lance, Can Zhang and Enrique Zuazua.
15:30-16:10 Jingrui Niu (HIT)
Title: The periodic KdV equation with control on spacetime measurable sets
Abstract: In this talk, we will study the local exact controllability of the KdV equation on the torus around equilibrium states, where both the spatial and the temporal control regions are sets of positive measure. First, we consider the linearized KdV equation and adapt a new method to prove the observability inequality on space-time measurable sets. This approach is also applicable to a broad class of dispersive equations on torus. Then we construct the control operator for the mass-conserved KdV equation on torus and finally establish the local controllability around equilibrium via a fixed-point argument. This is a joint work with Ming Wang and Shengquan Xiang.
16:20-16:40 Break（中场休息）
16: 40-17:20 Jacques Smulevici (SU)
Title: Time-periodic solutions of non-linear geometric wave equations
Abstract: I will present several results, obtained in collaboration with Athanasios Chatzikaleas, concerning the analysis of time-periodic solutions of several non-linear geometric wave equations, such the cubic conformal wave equations or the Yang-Mills equations on the 3-sphere. I will also explain the connection with an open problem in general relativity, the construction of time-periodic solutions to the Einstein-scalar field equations close to the Anti-de-Sitter spacetime. I will end the talk will end with a result concerning quasi-periodic Klein-Gordon equations on the circle, for which we prove, via the construction of special coordinates respecting the quasi-periodicity, the full reducibility of the operator. This can be viewed as a preliminary step in order to address KAM theory type problems for quasi-linear wave equations.
17: 30-18:10 Dominik Adolf (HIT)
Title: Towards an equiconsistency at the level of supercompact cardinals (without choice)
Abstract: Supercompact cardinals are at the center of many questions in Set Theory today. A longstanding open problem is to construct canonical inner models with supercompact cardinals. It was long believed that this could be achieved by studying failures of the combinatorial principle square. Recent results by Blue, Larson, and Sargsyan have shown that this is impossible. They construct a certain model in which the least uncountable cardinal is supercompact (Choice necessarily fails in such a model). They then force a model of choice in which square fails everywhere. This could mean that computing the exact consistency strength of the least uncountable cardinal being supercompact is within reach. We want to discuss some of the challenges along the road towards this goal.
