Date/Time : 12 May 2026 14:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : LIU Jie, Chinese Academy of Sciences

I will report a joint work with Baohua Fu proving that most Hamiltonian reductions of cotangent bundles are affine closures of cotangent bundles, together with some applications.

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Date/Time : 04 May 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Chung Pang Mok , Shanghai Institute for Mathematics and Interdisciplinary Sciences

In this talk we discuss the Birch and Swinnerton-Dyer formula modulo square of rational numbers for the quadratic twist family of a given elliptic curve over Q. In particular we show the following: let E be a semistable elliptic curve over Q with conductor N, whose analytic rank is at most one, then for any positive fundamental discriminant D that is relatively prime to N, such that the quadratic twist E^D again has analytic rank at most one, we have that the Birch and Swinnerton-Dyer formula modulo square of rational numbers holds for E if and only if it holds for E^D.

Joint work with Alexander Barrios.

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Date/Time : 29 Apr 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Juncheng Wei, The Chinese University of Hong Kong

In 2023, one year before his death, H. Brezis posted 28 open questions which he described as “challenging and difficult”. In this talk I will give complete answer to the first open question—Problem 1.1 on Brezis-Nirenberg problem on three dimensional unit ball, and the seventh open question—Problem 3.1 on harmonic map equation on disk.

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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 : 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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Date/Time : 06 Apr 2026 10:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Siyuan Tang, Xiamen University

We study the dynamics of $SL_{2}(\mathbb{R})$ on the stratum of translation surfaces. In particular, we obtain an effective closing lemma on $\mathcal{H}(2)$. More precisely, we show that unless a small discriminant Teichmüller curve near $x\in\mathcal{H}(2)$, the geodesic push-forward of horocycle orbit $a_{t}u_{[0,1]}x$ has the discretized fractal dimension near 1 in a direction transverse to the $SL_{2}(\mathbb{R})$-orbit. The proofs make use of spectral gaps, of the Margulis function technique, and of the classification of Teichmüller curves in $\mathcal{H}(2)$.

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