Date/Time : 04 Feb 2026 15:00
Venue : IMS Executive Seminar Room (S17 Level 3)
Speaker : Zhang Pingwen, Wuhan University and Peking University

Real numbers underpin mathematical research and the understanding of natural phenomena. The real number set comprises rational numbers (a measure-zero set) and irrational numbers (a full-measure set), implying that systems governed by irrational numbers are more prevalent. However, current computers cannot exactly store or represent irrational numbers, rendering numerical computations for irrational-dominated systems susceptible to Diophantine errors—incurred when approximating irrationals with rationals. Such errors significantly compromise numerical results. In this talk, we analyze the mechanism of Diophantine error and its impact on numerical computations. We also develop an approximation theory for multi-dimensional quasiperiodic functions with Diophantine frequencies when approximated by periodic functions. To avoid Diophantine errors, we propose two novel algorithms: the projection method and the finite points recovery method, which extend high-precision numerical computation from the rational to the real domain. Leveraging the ergodic and arithmetic properties of irrational numbers, we establish the mathematical foundations of these algorithms. Furthermore, we present their applications to several irrational-dominated scientific problems to discover new physical phenomena, including quasicrystals and their phase transitions, interfacial structures in materials, and quasiperiodic Schrödinger operators.

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Date/Time : 04 Feb 2026 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Gunter Schuetz, University of Lisbon

The symmetric Dyson exclusion process (SDEP) is a stochastic interacting particle system with exclusion and long-range, Coulomb-type interactions that emerge both as the maximal-activity limit of the symmetric simple exclusion process and as a discrete version of Dyson’s Brownian motion on the unitary group. Exploiting an exact ground-state (Doob) transform, we map the stochastic generator of the SDEP onto the spin-1/2 XX quantum chain, which in turn admits a free-fermion representation. This allows for proving an explicit formula for the time evolution of the expected microscopic particle density. At macroscopic scales we conjecture that the SDEP displays ballistic (Eulerian) scaling and non-local hydrodynamics where the current is a genuinely non-local functional of the density given by a Hilbert transform. This non-local one-field description is equivalent to a local complex Burgers equation for finite particle density. Closed evolution formulas allow us to solve the melting of single and double block initial states, producing limit shapes and arctic curves that agree with large-scale Monte Carlo simulations. The model thus offers a tractable example of emergent non-local hydrodynamics driven by long-range interactions.

(joint work with J. Dubail and A. Zahra)

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Date/Time : 02 Feb 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Yihang Zhu, Tsinghua University

The Langlands-Kottwitz method seeks to express Frobenius-Hecke traces on the cohomology of Shimura varieties in terms of objects in local harmonic analysis which enter the Arthur-Selberg trace formula, namely orbital and twisted orbital integrals. As a local analogue, we present a formula relating the cohomology of local Shimura varieties with twisted orbital integrals. This formula bridges the point-counting formula for Shimura varieties with the point-counting formula for Igusa varieties, a manifestation of the Mantovan product relation. As an application of our local formula, we explain a new categorical-Langlands-based approach towards Rapoport’s conjecture on the vanishing of certain twisted orbital integrals, which is itself a key ingredient in the global Langlands-Kottwitz method for a non-quasi-split prime. This is joint work with Rong Zhou.

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Date/Time : 30 Jan 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Robin van Haastrecht, The University of Gothenburg

We study degenerate principal series representations of the split real group $G_{2(2)}$ induced from a character of a maximal parabolic subgroup whose unipotent radical is a Heisenberg group. Using the Lie algebra action on the space of $K$-finite vectors, we find the points of reducibility and the complementary series. The minimal representation and a limit of discrete series are identified as kernel of the corresponding Knapp–Stein intertwining operator. Moreover, we show that some quaternionic discrete series representations occur as the subrepresentation on which the intertwining operator vanishes of order $2$.

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Date/Time : 30 Jan 2026 12:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Philippe Codognet, Sorbonne University

Introduced in 1965 by John P. Costas for SONAR and RADAR applications, the notion of Costas Arrays, i.e., 2-dimension arrays with optimal autocorrelation properties, is a hard combinatorial problem with many applications.
Although several methods have been designed for constructing Costas Arrays, e.g. Golomb or Welch methods, there is no general method to construct all Costas Arrays for any given size n, which is an NP-complete problem, and thus one has to resort to exhaustive search for finding all Costas Arrays of size n.

All Costas Arrays up to size 29 have been discovered, some for size 30 and 31, but the existence of a Costas Array of size 32 is still an open problem after more than 60 years. This makes the Costas Array Problem (CAP) an interesting challenge for quantum computing, in particular for quantum optimization, which is the modeling and solving of combinatorial problems with quantum computations. In this domain, Quadratic Unconstrained Binary Optimization (QUBO) has emerged as a common paradigm for modeling and solving combinatorial problems either by quantum annealing (e.g. with the D-Wave quantum computers) or by the Quantum Optimization Approximation Algorithm (QAOA, on gate-based quantum architectures).

We will present in this talk a new QUBO model for the CAP aimed at an implementation on quantum computers. A few years ago, a direct modeling of the CAP with Boolean variables has been proposed, which requires O(n^4) QUBO variables for a CAP instance of size n, that is, n^4 logical qubits on a quantum computer, but further reduction is indeed possible. We thus propose a new model which requires only O(n^3) variables for a CAP instance of size n, making thus medium-size instances tractable on current quantum annealing hardware, e.g. D-Wave Advantage systems. This new model consider the (usual) representation the CAP as an integer-based Constrained Optimization Problem, where the Costas Array is represented as a permutation of {1, . . . , n} and focuses on the property that if the so-called “difference table” constructed from a permutation p do not have any repeated value for any line, then p represents a Costas Array. This property of the difference table can be enforced in the QUBO model by defining adequate penalty expressions corresponding to the at-most-one constraints (one for each line of the difference table). These penalty expressions are then added to the objective function as well as the penalty expression corresponding to the overall constraint to be a permutation.

We will moreover present implementation results for this new model and a comparison with the previous direct model, on D-Wave quantum annealer and on the quantum-inspired Fixstars Amplify Annealing Engine.

This seminar is a joint event between CQF and NUS Integrated Quantum & AI Computing Consortium.

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Date/Time : 30 Jan 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Soon Hoe Lim, KTH

Flow matching has emerged as a powerful paradigm for generative modeling. From the viewpoint of dynamical measure transport, it constructs continuous-time ODE samplers by prescribing probability paths that connect a base and a target distribution. In this talk, we discuss both the potential and pitfalls of flow matching for probabilistic forecasting of dynamical systems.

We observe that forecasting performance is highly sensitive to the choice of probability path, motivating principled constructions that lead to improved computational efficiency and predictive performance on spatio-temporal dynamical system benchmarks. We then revisit flow matching in the empirical setting and analyze the structure of the induced velocity fields, uncovering connections between flow matching, memory effects, and nonparametric dynamical systems. This perspective leads to new sampling strategies and raises questions about the role of parameterization in learning dynamical systems from data.

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Date/Time : 28 Jan 2026 17:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Chong Chi Tat, National University of Singapore

This talk is a continuation and concluding part of the talk given in 2024/25. It concerns the problem of definable solutions of combinatorial principles such as the Cohesive Set Theorem, Ramsey’s Theorem and the Halpern-Lauchli Theorem over models of subsystems of second-order arithmetic. In a joint work with Wong Tin Lok reported here, we give a complete solution of this problem, as well as problem of the existence of a definable minimal degree over such models.

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Date/Time : 28 Jan 2026 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Swee Hong Chan, Rutgers University

Consider the set of positive integers representing the number of spanning trees in simple graphs with n vertices. How quickly can this set grow as a function of n? In this talk, we discuss a proof of the exponential growth of this set, which resolves an open problem of Sedlacek from 1966. The proof uses a connection with continued fractions and advances towards Zaremba’s conjecture in number theory. This is joint work with Alex Kontorovich and Igor Pak. This talk is intended for general audience.

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Date/Time : 28 Jan 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Taoran He, Institut des Hautes Études Scientifiques

In this talk, I will present our recent work on the stability of Kasner solutions for the Einstein-Maxwell-scalar field-Vlasov system in 1+3 dimensions. This system incorporates gravity, electromagnetic, weak and strong interactions for the initial stage of our universe. The inclusion of the Vlasov field introduces several new challenges. By observing detailed mathematical structures and designing new delicate arguments, we identify a new strong sub-critical regime and prove the nonlinear stability with Kasner exponents lying in this entire regime. Our results extend the work of Fournodavlos-Rodnianski-Speck from the Einstein-scalar field system to the physically more complex system with the Vlasov field. This is joint work with Xinliang An and Dawei Shen.

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