Date/Time : 01 Aug 2024 15:00
Venue : S17 #04-05 (SR2)
Speaker : Armin Schikorra, University of Pittsburgh

n-Laplace systems with antisymmetric potential are known to govern geometric equations such as n-harmonic maps between manifolds and generalized prescribed H-surface equations. Due to the nonlinearity of the leading order n-Laplace and the criticality of the equation they are very difficult to treat.

I will discuss some progress we obtained, combining stability methods by Iwaniec and nonlinear potential theory for vectorial equations by Kuusi-Mingione.

Joint work with Dorian Martino

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Date/Time : 31 Jul 2024 14:00
Venue : S17 #04-05 (SR2)
Speaker : Jan M. Swart, The Czech Academy of Sciences

In a classical game two players, Alice and Bob, take turns to play n moves each. Alice starts. For each move each player has two options, 1 and 2. The outcome is determined by the exact sequences of moves played by each player. Prior to the game, a winner is assigned to each of the 2^{2n} possible outcomes in an i.i.d. fashion, where p is the probability that Bob is the winner for a given outcome. Then it is known that there exists a value 0<p_c<1 such that the probability that Bob has a winning strategy for large n tends to one if p>p_c and to zero if p<p_c. We study a modification of this game for which the outcome is determined by the exact sequence of moves played by Alice as before, but in the case of Bob all that matters is how often he has played move 1. We show that also in this case, there exists a sharp threshold p’_c that determines which player has with large probability a winning strategy in the limit as n tends to infinity.

Joint work with Anja Sturm and Natalia Cardona-Tob\’on (G\”ottingen).

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Date/Time : 30 Jul 2024 15:00
Venue : S17 #04-05 (SR2)
Speaker : Min XU, Carnegie Mellon University

Cryo-electron tomography (cryo-ET) 3D imaging technology captures a 3D image of a single cell’s subcellular structures at sub-molecular resolution and in a near-native state. It provides unprecedented opportunities for systematically studying the native spatial organization of subcellular structures, especially macromolecules. However, cryo-ET has high structural complexity and imaging limits, such as high structural diversity and crowding, low signal-to-noise ratio, and missing values. These have made the automated systematic analysis of such images extremely difficult. I will present our recent efforts to develop methods for automated analysis of cryo-ET data.

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Date/Time : 24 Jul 2024 15:00
Venue : S17 #04-05 (SR2)
Speaker : Shidong Jiang, Flatiron Institute

In this talk, we will first present an overview of fast integral equation methods (FIEMs). Fast algorithms, such as the fast multipole methods and their descendants, have made profound impacts on many areas of scientific computing. Boundary integral equations of the second kind are the natural formulation for boundary value problems of elliptic partial differential equations due to the reduction of dimensionality by one, automatic satisfaction of conditions at infinity for exterior and scattering problems, and well conditioning. The computational bottleneck that arises because the resulting linear system is dense due to the nonlocal and long-range nature of integral operators is largely removed by fast algorithms. FIEMs have been highly successful in solving a large class of problems in fluid mechanics, elasticity, acoustics, and electromagnetics.

Second, we introduce a new class of multilevel, adaptive, dual-space methods for computing fast convolutional transforms. The DMK (dual-space multilevel kernel-splitting) framework uses a hierarchy of grids, computing a smoothed interaction at the coarsest level, followed by a sequence of corrections at finer and finer scales until the problem is entirely local, at which point direct summation is applied. Unlike earlier multilevel summation schemes, DMK exploits the fact that the interaction at each scale is diagonalized by a short Fourier transform, permitting the use of separation of variables without relying on the FFT. The DMK framework substantially simplifies the algorithmic structure of the fast multipole method (FMM) and unifies the FMM, Ewald summation, and multilevel summation, achieving speeds comparable to the FFT in work per grid point, even in a fully adaptive context.

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Date/Time : 24 Jul 2024 15:00
Venue : S17 #04-04 (SR3)
Speaker : Chen Qile, Boston College

Gauged Linear Sigma Models introduced by physicists in the 90’s is a way of counting curves in critical loci of a holomorphic function called superpotentials. In this talk, I will report on a joint project in progress with Felix Janda and Yongbin Ruan on computing Gauged Linear Sigma Models via logarithmic compactifications. Our method will lead to quantum lefschetz formulas in all genera, relating Gromov-Witten invariants of complete intersections with enumerative geometry of their ambient spaces. Furthermore the correction terms in these formulas are virtual counts of “generalized special linear series”. In case of Fano complete intersections, we show that the vanishing of these correction terms are controlled by invariants from birational geometry.

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Date/Time : 17 Jul 2024 15:00
Venue : via Zoom
Speaker : Feng Shao, Peking University

Join Zoom Meeting
https://nus-sg.zoom.us/j/82730991505?pwd=LEzOeoXXrYPflm2EVK5xKzpiQCi6Pt.1

Meeting ID: 827 3099 1505
Passcode: 008679

In this talk, I will discuss the joint work with Dongyi Wei and Zhifei Zhang on the construction of self-similar smooth imploding solutions of isentropic relativistic Euler equations with isothermal equation of state $p=\frac1\ell\varrho$ for all $\ell>1$ in physical space dimension $d=2,3$ and for $\ell>1$ close to 1 in higher dimensions. This work is a crucial step toward solving long-standing open problem: finite time blow-up of the supercritical defocusing nonlinear wave equation.

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Date/Time : 17 Jul 2024 17:00
Venue : LT33 (S17 Level 2)
Speaker : Wojciech Woloszyn, University of Oxford

Two features of the Ultimate L are that it is forcing invariant and compatible with large cardinals. The resurrection principle stabilizes forcing out albeit mildly. The latter can be refuted from the existence of a large cardinal way below I0. What is the bearing of this on the status of large cardinals and the axiom V=Ultimate L? An interesting picture unfolds.

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Date/Time : 16 Jul 2024 15:30
Venue : LT33 (S17 Level 2)
Speaker : Nishant Chandgotia, Tata Institute of Fundamental Research - Centre for Applicable Mathematics

When can a given subset S be tiled by rectangular tiles in Z^2? This is an old question and for answering it Conway and Lagarias introduced certain groups which are now known as the Conway-Lagarias group (1990). Together with some analytic conditions, Thurston noticed that these questions can be answered completely in certain situations. This later formed the basis for understanding what uniformly random tiling of regions looked like (for instance in the results from Cohn, Kenyon and Propp from 2001). In 1995, Klaus Schmidt realised that this was related to a certain cohomology of dynamical systems and initiated its formal study. We will talk about such questions in the context of graph homomorphisms on the Z^d lattice and see how it relates to the word problem of finitely presented groups.

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Date/Time : 12 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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