Thu, 23 Apr 2026
17:00
17:00
L4
Conjugacy of trivial autohomeomorphisms of $\beta N\setminus N$.
Ilijas Farah
(York University, Toronto)
Abstract
An autohomeomorphism of the Čech--Stone remainder $\beta N\setminus N$ is called trivial if it has a continuous extension to a map from $\beta N$ into itself. Such map is determined by an almost permutation, which is a bijection between cofinite subsets of $N$. By results of W. Rudin and S. Shelah, the question whether nontrivial autohomeomorphisms of $\beta N\setminus N$ exist is independent from ZFC. We will be considering the so-called rotary autohomeomorphisms. An autohomeomorphism is called rotary if it corresponds to a permutation of $N$ all of whose cycles are finite. If all autohomeomorphisms are trivial, then the problem of their conjugacy is also trivial (in the usual sense of the word). However the Continuum Hypothesis makes the conjugacy relation nontrivial. While our results are somewhat incomplete, they suffice to decide whether for example the rotary autohomeomorphisms whose cycles have lengths $2^{2n}$, for $n\in N$, and $2^{2n+1}$, for $n\in N$, are conjugate. This is a joint work with Will Brian.
Thu, 23 Apr 2026
11:00
11:00
L4
Upper bound to the GK-dimension for p-adic Banach representations with infinitesimal character
Reinier Sorgdrager
(University of Amsterdam and Université Paris-Saclay)
Abstract
Let p>2 and K be a finite extension of Q_p. In recent work I have shown that an admissible p-adic Banach representation of GL2(K) has Gelfand-Kirillov dimension at most the degree [K:Q_p] as soon as its locally analytic vectors have an infinitesimal character. In work yet to appear I adapt its method to 'p-adic Banach representations in families with infinitesimal characters in families' -- still for GL2(K).
I will briefly motivate the result by some consequences to the p-adic Langlands program, such as a generalization of the GK-bound of Breuil-Herzig-Hu-Morra-Schraen beyond K unramified. Then I will give a quick overview of the above notions and try to present the key idea of the proof, for a single representation and with K=Q_p.
Tue, 02 Jun 2026
14:00
14:00
L4
Mon, 04 May 2026
16:30 -
17:30
L4
Mon, 01 Jun 2026
14:15
14:15
L4
Mon, 11 May 2026
16:30 -
17:30
L4
Derivation of the fourth order DLSS equation with nonlinear mobility via chemical reactions
André Schlichting
(University Ulm)
Abstract
We provide a derivation of the fourth-order DLSS equation based on an interpretation as a chemical reaction network. We consider on the discretized circle the rate equation for the process where pairs of particles sitting on the same side jump simultaneously to the two neighboring sites, and the reverse jump where a pair of particles sitting on a common site jump simultaneously to the side in the middle. Depending on the rates, in the vanishing mesh size limit we obtain either the classical DLSS equation or a variant with nonlinear mobility of power type. We identify the limiting gradient structure to be driven by entropy with respect to a generalization of the diffusive transport type with nonlinear mobility via EDP convergence. Furthermore, the DLSS equation with nonlinear mobility of the power type shares qualitative similarities with the fast diffusion and porous medium equations, since we find traveling wave solutions with algebraic tails and polynomial compact support, respectively.
Joint work with Alexander Mielke and Artur Stephan arXiv:2510.07149. The DLSS part is based on joints works with Daniel Matthes, Eva-Maria Rott and Giuseppe Savaré.
Mon, 04 May 2026
14:15
14:15
L4
A universal Higgs bundle moduli space
Nigel Hitchin
((Mathematical Institute University of Oxford))
Abstract
The moduli space of Higgs bundles on a compact Riemann surface C for a group G is diffeomorphic to the character variety of representations
of the fundamental group in G. One description depends on the complex structure of C, the other is purely topological. Using a natural symplectic Ehresmann connection we show how to build the complex structure on the family of Higgs bundle moduli spaces over Teichmuller space and derive some consequences for the energy of the associated harmonic maps.