Date/Time : 11 Sep 2024 17:00
Venue : S17 #04-04 (SR3)
Speaker : Kihara Takayuki, Nagoya University

The theories of degrees of unsolvability and realizability interpretation both have long histories, having both been born in the 1940s. S. C. Kleene was a key figure who led the development of both theories. Despite having been developed by the same person, there seems to have been little deep mixing of these theories until recently. In this talk, we will reconstruct the theory of degrees of unsolvability from the perspective of realizability theory.

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Date/Time : 11 Sep 2024 14:00
Venue : S17 #04-05 (SR2)
Speaker : Tran Chieu-Minh, National University of Singapore

A locally compact group is nonunimodular if it has no Haar measure (i.e. every left Haar measure m is not right invariant). Considering doubling ratio m(AA)/m(A) initially looks strange on such exotic setting but turns out to be crucial even for the purpose of studying doubling on unimodular locally compact groups. In this talk I will discuss this issue further including a recently published result in this direction. ( Based on joint works with Yifan Jing and Ruixiang Zhang).

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Date/Time : 11 Sep 2024 15:00
Venue : S17 #04-06 (SR1)
Speaker : Binyong Sun, IASM, Zhejiang University

After introducing some basic notions in the representation theory of classical Lie groups, I will explain three results in this theory: the multiplicity one theorem for classical groups, the conservation relation for local theta correspondence, and the non-vanishing hypothesis at infinity for Rankin-Selberg convolutions. Some relevant or consequent results will also be explained.

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Date/Time : 11 Sep 2024 16:30
Venue : S17 #06-11 (SR6)
Speaker : Yang Liu, National University of Singapore

Can we build a single large model for a wide range of PDE-related scientific learning tasks? Can this model generalize to new PDEs without any fine-tuning? In-context operator learning and the corresponding model In-Context Operator Networks (ICON) represent an initial exploration of these questions. We present a detailed methodology for solving PDE problems with ICON, and show how a single ICON model can make forward and reverse predictions for different equations with different strides, provided with appropriately designed data prompts. We show positive evidence for the questions above, through a study on 1D scalar nonlinear conservation laws, a family of PDEs with temporal evolution. In particular, we show that an ICON model trained on conservation laws with cubic flux functions can generalize well to some other flux functions of more general forms, without fine-tuning. We will also discuss different theoretical interpretations of in-context learning.

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Date/Time : 11 Sep 2024 15:00
Venue : S17 #05-11 (SR5)
Speaker : Yuxuan Wang, Tsinghua University

First examined by Riemann in 1860 in one-dimensional space, the Riemann problem has since been extensively studied and advanced by numerous scholars. Our talk will investigate the interaction of two approaching shocks in the context of spherical symmetry in three-dimensional space, presuming the fluid to be ideally barotropic. We will outline the proof of the local existence, uniqueness, and higher regularity of the solution to the shock interaction problem.

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Date/Time : 09 Sep 2024 17:00
Venue : S17 #04-05 (SR2)
Speaker : Ichiro Shimada, Hiroshima University

The Ap\’ery-Fermi pencil is a certain one-dimensional family of complex affine surfaces related to a Fermi surface in solid state physics. This pencil is also connected to Ap\’ery’s proof of the irrationality of the zeta value at s=3.

A general member of the Ap\’ery-Fermi pencil is birational to a K3 surface with Picard number 19. We calculate the automorphism group of this K3 surface by means of Borcherds’ method.

I also present some general algorithms that may be useful in computational algebraic geometry.

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Date/Time : 09 Sep 2024 16:00
Venue : S17 #05-11 (SR5)
Speaker : Jean-Bernard Lasserre, LAAS-CNRS

We briefly describe the Christoffel-Darboux (CD) kernel and the Christoffel function (CF). While well-known tools in orthogonal polynomials and approximation theory, it is only recently that CF’s properties have been shown to be very useful and powerful (as well as easy to implement) to help solve some problems

— in data analysis and datra mining where the underlying (empirical) measure is usually discrete, e.g. for outlier detection, support inference, density approximation, and

— in approximation of discontinuous functions.

Finally we will also briefly describe some (in the author’s opinion surprising) links of the CF with seemingly less disconnected areas (Pell equation, equilibrium measure, convex optimization and positivity certificates).

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Date/Time : 05 Sep 2024 16:00
Venue : S17 #05-12 (SR4)
Speaker : Ning Li, Nankai University

The notion of transfer is a way to relate representation theory of different real forms of a complex semisimple Lie group. In this talk, I will explicitly describe the transfer of \theta(1) of Sp(2n,R) in the case of non-stable range via the study of K-types. As a corollary, we get certain compatibility of local theta correspondence and the transfer functor, and every unitary irreducible constituent of degenerate principal series of maximal Gelfand-Kirillov dimension is a derived functor module, which coincide with the results of Matumoto-Trapa for the case of Sp(p,q), SO*(2n), and U(m,n).

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Date/Time : 04 Sep 2024 14:00
Venue : S17 #04-05 (SR2)
Speaker : Peng Fei, National University of Singapore

A quasi-kernel of a digraph is an independent set Q such that every vertex can reach Q in at most two steps. The 48-year-old small QK conjecture says that every sink-free digraph contains a quasi-kernel of size at most n/2. Spiro posed the large QK conjecture, which states that every digraph contains a quasi-kernel Q such that |N^-[Q]| ≥ n/2, and showed that it follows from the small QK conjecture. We show that the converse is true with a weaker constant. We also show that every sink-free digraph contains a quasi-kernel of size at most (1−1/k)n, where k is the digraph’s kernel-perfect number, generalizing a result by Kostochka, Luo and Shan. Joint work with Ai and Liu.

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