Date/Time : 12 Jul 2024 15:00
Venue : S17 #04-05 (SR2)
Speaker : Zhang Zhen, Southern University of Science and Technology

Anisotropic surface diffusion is recently investigated in detail from both modeling and numerical perspectives. While sharp-interface models provide a clear description of the problem, it introduces difficulties in numerical simulations especially when there are topological changes. In this talk, we will present a phase-field approach for modeling anisotropic surface diffusions. We first consider the equilibrium problem of energy minimization. By employing a three-operator splitting technique, we could numerically compute the equilibrium shapes of crystals (ESC) using an optimization approach with mathematical convergence. Then we propose a second-order mass preserving dynamic model as a gradient flow of the anisotropic energy for simulating surface diffusion processes. For surface diffusions in contact with solid substrates, we discuss a regularized thin film model as an approximation of the sharp-interface problem. Numerical results demonstrate the good convergence of these models.

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Date/Time : 10 Jul 2024 14:00
Venue : S17 #04-04 (SR3)
Speaker : Nishant Chandgotia, TIFR CAM (Bangalore)

The dimer model, also referred to as domino tilings or perfect matching, are tilings of the Z^d lattice by boxes exactly one of whose sides has length 2 and the rest have length 1. This is a very well-studied statistical physics model in two dimensions with many tools like height functions and Kasteleyn determinant representation coming to its aid. The higher dimensional picture is a little daunting because most of these tools are limited to two dimensions. In these series of talks I will describe some recent progress in 3 dimensions where we show a large deviations principle for dimer tilings analogous to those by Cohn, Kenyon and Propp (2000). This is joint work with Scott Sheffield and Catherine Wolfram.

The talks should be accessible to a general audience but it will help to have working knowledge of probability and basic ergodic theory.

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Date/Time : 08 Jul 2024 16:00
Venue : S17 #04-06 (SR1)
Speaker : Panel Discussion: Various speakers,

The leap from higher education to industry is a pivotal stage for many graduate students. Emphasising the necessity of an interdisciplinary approach and the application of the robust analytical skills honed during graduate studies, this panel discussion offers a comprehensive exploration of the journey that awaits MSc and PhD graduates who are looking to bridge the gap between academic accomplishment and professional fulfilment in the industry. Panellists will provide candid reflections on their personal pathways, highlighting the obstacles they encountered and the successes they achieved within various industrial domains. Attendees of the session will be encouraged to engage with live inquiries and raise pertinent topics for discussion. Discussions will revolve around the symbiotic relationship between advanced academic preparation and industry expectations, strategic planning for entering the corporate sector, the diverse opportunities ranging from employment in small to large-scale organisations to the launch of deep tech ventures, as well as the innovative trends and fruitful careers found in today’s industrial research and development.

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Date/Time : 04 Jul 2024 14:00
Venue : S16 #03-05/06
Speaker : Libo Li, University of New South Wales, Sydney

We study the upper and lower bounds for prices of European and American style options with the possibility of an external termination, meaning that the contract may be terminated at some random time. Under the assumption that the underlying market model is incomplete and frictionless, we obtain duality results linking the upper price of a vulnerable European option with the price of an American option whose exercise times are constrained to times at which the external termination can happen with a non-zero probability. Similarly, the upper and lower prices for an vulnerable American option are linked to the price of an American option and a game option, respectively. In particular, the minimizer of the game option is only allowed to stop at times which the external termination may occur with a non-zero probability.

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Date/Time : 01 Jul 2024 16:00
Venue : S17 #04-04 (SR3)
Speaker : Baohua Fu, The Institute of Mathematics, CAS, Beijing

A smooth projective variety X is called rigid if any deformation of X is isomorphic to itself. The first example is the projective space, but in general, it is a subtle and difficult problem to prove the deformation rigidity. I’ll report some recent progress on this problem. Part of this talk is based on joint works with Yifei Chen(Chinese Academy of Sciences) and Qifeng Li (Shandong Univ).

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Date/Time : 20 Jun 2024 14:00
Venue : S17 #04-05 (SR2)
Speaker : Sunil Chebolu, Illinois State University

More than 50 years ago, Fuchs asked which abelian groups can be the group of units of a commutative ring? Though progress has been made, the question remains open. I will present an overview of my joint work with Keir Lockridge on this problem. We answered this question for various classes of groups including indecomposable abelian groups, dihedral groups, quaternion groups and some p-groups. This work also gave us several new characterizations of Mersenne primes and Fermat primes.

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Date/Time : 19 Jun 2024 14:00
Venue : S17 #04-04 (SR3)
Speaker : Yuan Yancheng, Hong Kong Polytechnic University

Convex clustering model has attracted growing attention in the machine learning community. In this talk, we will introduce some recent progress of convex clustering model on model performance and numerical computation. Moreover, we will introduce a newly developed solver for solving the convex clustering model with GPU acceleration.  

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Date/Time : 18 Jun 2024 16:00
Venue : S17 #04-05 (SR2)
Speaker : Weng Kee Wong, University of California at Los Angeles

This talk first reviews mathematical techniques for constructing various types of optimal experimental designs before I present applications to design early phase clinical trials. For more complex problems, the methodology is increasingly combined with nature-inspired metaheuristics, which are assumptions free, general-purpose optimization algorithms motivated by nature, like animal behavior. After a quick overview of metaheuristics, I use MATLAB and demonstrate how these algorithms can efficiently find multiple-objective optimal designs for a biomedical problem. E-optimal designs are a minimax type of optimal designs that pose particular mathematical challenges and I discuss some of them, including a continuing effort to find a practically useful algorithm for generating E-optimal designs and has a proof of convergence.

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Date/Time : 14 Jun 2024 15:00
Venue : S17 #04-04 (SR3)
Speaker : Greg McShane, Institut Fourier

The modular surface $\mathbb{H}/\Gamma,\, \Gamma= \math rm{SL}(2,\mathbb{Z})$ has many covers -for example the three punctured torus $\mathbb{H}/\Gamma(2)$ and the once punctured torus $\mathbb{H}/\Gamma’$.

We will discuss how classical Diophantine approximation can be interpreted in terms of the behavior of geodesics on the once-punctured torus and a geometric reformulation of the Frobenius uniqueness conjecture. We will then give an account of two theorems of Fermat in terms of the automorphisms of $\mathbb{H}/\Gamma(2)$:
– if $p$ is a prime such that $4|(p-1)$ then can be written as a sum of squares $p = c^2 + d^2$
– if $p$ is a prime such that $3|(p-1)$ then can be written as $ p = c^2 +cd + d^2$

Finally, we will discuss possible extensions to surfaces of the form $\mathbb{H}/\Gamma_0(N)$.

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