Date/Time : 22 Apr 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Phan Quoc Vuong,

Blow-up of a graph is a useful trick in extremal graph theory, replacing every vertex with a finite collection of copies so that the copies of two vertices are adjacent if and only if the originals are. In this talk, I will explain how to extend the blow-up trick to general combinatorial objects, and discuss about its potential application, illustrated by a recent result related to hypergraph Turan problem.

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Date/Time : 21 Apr 2026 12:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Ulrich Horst, Humboldt University, Berlin

We establish a simple microstructure foundation for rough log-normal volatility models such as the rough Bergomi model. Unlike in earlier microstructure model we do not assume that that market orders arrive according to a heavy-tailed Hawkes process. Instead, we assume that orders arrive according to a standard Poisson process but have long lasting impact on asset price volatility. After suitable scaling the logarithmic volatility converges weakly to fractional Brownian motion mit H<1/2. Weak convergence rates are also established. The talk is based on joint work with Paul Hager, Thomas Wagenhofer and Wei Xu.

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Date/Time : 17 Apr 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Joven Jia Xuan Teo, National University of Singapore

The nilpotent orbits of a Lie algebra are important objects relevant to representation theory, for instance in the definition of wavefront sets. If the algebra in question is one arising from a nondegenerate symmetric, symplectic, or Hermitian space over a topological field, it is known that the nilpotent orbits can be parametrised by objects called admissible labelled partitions. Furthermore, one can define in a reasonably simple way a partial ordering of these partitions that conjecturally corresponds to the closure ordering of the nilpotent orbits.

In this talk, we will introduce these admissible labelled partitions and the partial ordering defined on them. We then summarise the ideas in Djokovic’s proof of the real case. Finally, we discuss the obstacles in attempting to generalise these ideas to the p-adic case and beyond.

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Date/Time : 15 Apr 2026 16:30
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Zhang Junyi, Nanyang Technological University

Quantum Approximate Optimization Algorithm (QAOA) was proposed as a variational quantum algorithm for solving combinatorial optimization problems. In this talk, I will discuss some recent observations in quantum circuit dynamics of QAOA. We identify three dynamical phases in the quantum circuits: 1) quasi-adiabatic phase, 2) quantum chaotic phase, and 3) shallow circuit phase. Particularly, we find that the quasi-adiabatic phase and the shallow circuit phase are separated by a dynamical quantum critical point indicated by the entanglement entropy. Moreover, the quantum chaotic phase emerges in digitized quantum circuit while absent for continuous unitary evolution. Our study calls for better understanding of quantum algorithms realized in quantum circuits.

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Date/Time : 15 Apr 2026 16:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Tomoyuki Abe, Kavli IPMU, Tokyo

Deligne showed that the diagonal series of an algebraic power series of n variables over a field of positive characteristic remains algebraic. He deduced this theorem using geometric method in the case n=2, and showed the general case using purely algebraic method. However, he expected a more direct proof of that fact, and gives a conjectural bound of the degree of algebraicity. The conjectural bound had been verified by Adamczewski and Bell using elementary method. We revisit this question using arithmetic D-module. This is a joint work with R. Crew.

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Date/Time : 10 Apr 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Samuel Hon, National University of Singapore

The closures of conjugacy classes in classical real linear lie groups were determined by Djokovic in his 1982 paper. Through a series of theorems, the proof reduces to mainly combinatorial arguments which aren’t difficult, but tedious to check. In this talk, I will discuss how we are formalizing the proof in LEAN and how this makes the checks simpler. I will begin with a short introduction on the proof, how and why LEAN works, and how we can leverage AI to simplify and speed up the process.

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Date/Time : 08 Apr 2026 17:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Frank Stephan, National University of Singapore

Many-one degrees and one-one degrees are basic degree structures in recursion theory and since Young’s result 1966, that every nonrecursive many-one degree either coincides with a one-one degree or embeds every possible countable linear order inside the structure of its one-one degrees, the question whether this is also true for partial orders received attention. Dëgtev showed in 1976 that this is true for all nonrecursive and recursively enumerable many-one degrees. Odifreddi in 1981 made the special case whether every nonrecursive many-one degree either contains an antichain of one-one degrees or coincides with a single one-one degree formally an open question. Since then for long time no progress was made until Batyrshin confirmed this for all limit-recursive many-one degrees. The present work shows this then also for all many-one degrees except for the greatest recursive many-one degree which is a special case by having a two-element antichain but not a longer one in its one-one degrees. Furthermore, the talk will also look at degree structures between one-one and many-one, namely the finite-one and bounded finite-one degrees. Finite-one degrees were introduced by Maslova 1979, but up to now did not find the attention they deserved.

This is joint work of Linus Richter, Frank Stephan and Xiaoyan Zhang.

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Date/Time : 08 Apr 2026 16:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Xiangqian Yang, Peking University

Clozel, Harris and Taylor proposed a generalized Ihara’s lemma for definite unitary groups. In this talk, we prove some cases of their conjecture under the assumption of banal coefficients. The proof relies on the unipotent categorical local Langlands correspondence established by Zhu. We also discuss certain properties of the coherent sheaf associated to the space of automorphic forms under the categorical local Langlands functor.

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Date/Time : 08 Apr 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Fabrizio Bianchi , University of Pisa, Italy

Around 1980, Ruelle gave an explicit second-order expansion at c=0 of the Hausdorff dimension of the Julia set of the quadratic family f_c(z)=z^2+c. McMullen later extended this result to polynomial perturbations of z^d for arbitrary degree d. I will discuss an analogue of this problem and formula for skew-product maps of C^2. This is a joint work with Yan Mary He.

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