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 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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Date/Time : 08 Apr 2026 16:30
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Feng Yue, Xi'an Jiaotong University

In this talk, I will introduce the long-time problem for the nonlinear Schrodinger equation (NLSE) with weak nonlinearity, which is characterized by with a dimensionless parameter. We solve the NLSE using various temporal discretization, including finite difference methods, exponential integrators and time-splitting methods combined with different spatial discretization. By introducing a new technique–Regularity Compensation Oscillation (RCO) which controls the high frequency modes by the regularity of the exact solution and analyzes the low frequency modes by phase cancellation and energy method, we carry out the improved uniform error bounds for the time-splitting Fourier pseudospectral method in the long-time regime. In addition, we design new exponential integrators for the low-regularity initial data and extend this result to other dispersive PDEs.

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Date/Time : 08 Apr 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Rao Rui, National University of Singapore

Consider the family of all k-element subsets of {1,…,n}. A subfamily F is called intersecting if any two of its sets have non empty intersection. Huang and Zhao proved that when n>2k, every intersecting family F contains an element i in [n] that belongs to at most {n-2 \choose k-2} members of F. This bound is tight, being attained by 1-star: all k-sets containing a fixed element.

We show that, for n sufficiently large (depending on k), all but at most k+1 elements of [n] have the same property: each of those elements appears in at most {n-2 \choose k-2} sets of F. The number k+1 is tight because of the Hilton-Milner construction of non trivial intersecting family.

This is joint work with Hao Huang.

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Date/Time : 08 Apr 2026 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Ho Boon Suan, National University of Singapore

Given a bipartite graph G with parts of size m and n, Ehrenborg conjectured in 2006 that the number of spanning trees in G is at most the product of all vertex degrees, divided by mn. We will discuss a linear-algebraic proof of this bound, including a characterization of when equality holds.

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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 : 06 Apr 2026 09:00
Venue : via Zoom
Speaker : Dilip Raghavan, National University of Singapore

Zoom: https://nus-sg.zoom.us/j/84790467054

Passcode: 547743 

There is an intimate relationship between Ramsey type theorems and ultrafilters on the natural numbers. On the one hand, ultrafilters can be used to prove Ramsey type theorems. On the other hand, Ramsey theoretic facts lead to new classes of ultrafilters. I will survey some aspects of this interplay, and present two recent consistency results involving ultrafilters with the Ramsey theoretic flavor.

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