Date/Time : 04 Feb 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Asbjørn Nordentoft, University of Copenhagen

To any thin subgroup of a finite co-volume Fuchsian group one can associate a hyperbolic orbifold with geodesic boundary. The projection of the geodesic boundary gives a stratification (or partition) of the set of all thin subgroups. In this talk I will explain how in some cases one can understand the fibers of this stratification. This is related to the problem of lifting closed geodesics ‘simply and separating’. In the case of the modular group this gives a new and geometric perspective on a construction of Duke, Imamoglu and Toth using (minus) continued fractions.

This is joint work in progress with Ser Peow Tan

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Date/Time : 04 Feb 2026 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Ngoc Cuong Nguyen, Kora Advanced Institute of Science & Technology

We study comprehensively local properties of functions in complex Sobolev spaces, introduced by Dinh and Sibony (2006), on a bounded open sub-set of C^n. The main tool is the corresponding functional capacity for the space which is inspired by the global one due to Vigny (2007). An inequality between this capacity and the Bedford-Taylor capacity for plurisubharmonic functions is proved, which is sharp as far as the exponents are concerned. Moreover, it is shown that the functional capacity is a Choquet capacity. The Alexander-Taylor type inequality for the capacity is also proved. This allows us to strengthen the results in the works of Dinh, Marinescu and Vu (2023), Vigny and Vu (2024).

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Date/Time : 04 Feb 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Dano Kim, Seoul National University

The theory of L2 extension theorems is a central topic in several complex variables with numerous applications to complex/algebraic geometry and complex analysis. They are analogous to vanishing theorems in algebraic geometry and often serve as a stronger counterpart of vanishing as exemplified in the proof of Siu’s invariance of plurigenera. In this talk, in the opposite direction, I will discuss how certain ideas from algebraic geometry are crucially used in answering a question raised by Demailly on understanding general L2 extension theorems, via the theory of log canonical pairs. This talk is partly based on joint work with Xu Wang (Trondheim).

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Date/Time : 04 Feb 2026 13:30
Venue : S16 #03-09
Speaker : Minwoo Chae, Pohang University of Science and Technology

In recent years, diffusion-based deep generative models have achieved remarkable success in various applications. In this talk, we present statistical theories for diffusion models within the framework of nonparametric structured density estimation. To address the curse of dimensionality in nonparametric density estimation, we assume that the underlying density function factorizes into several low-dimensional components. Such factorizable densities are common in important examples, such as Bayesian networks and Markov random fields. We prove that an implicit density estimator constructed from diffusion models achieves the minimax optimal convergence rate with respect to total variation. Technically, we design a novel network architecture, which includes convolutional neural networks as a special case, to construct a minimax optimal estimator.

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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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