Date/Time : 08 Oct 2021 16:00
Venue : via Zoom
Speaker : Siddhartha Mishra, ETH Zürich

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https://nus-sg.zoom.us/j/88995092115?pwd=UmxidFJqTzZyQ2JRLyt5SGNnaHhnUT09

Meeting ID: 889 9509 2115
Passcode: 309203

Abstract:  We will describe PINNs and illustrate several examples for using PINNs for solving PDEs. Our aim would be to elucidate mechanisms that underpin the success of PINNs in approximating classical solutions to PDEs by deriving rigorous bounds on the resulting error. Examples of a variety of linear and nonlinear PDEs will be provided including PDEs in high dimensions and inverse problems for PDEs.

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Date/Time : 08 Oct 2021 10:00
Venue : via Zoom
Speaker : Peter Mueller, University of Texas at Austin

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https://nus-sg.zoom.us/j/9775606531?pwd=cVZ6eTRYS3ZzVUlFNXRuSlhMVjJSUT09

Meeting ID: 977 560 6531
Passcode: 123321

Abstract: Nonparametric Bayesian methods allow for principled model-based inference on unknown functions, distributions and structures without restriction to specific parametric models. The flexible prediction rules and the more realistic and complete description of related uncertainties are useful in many examples of clinical trial design and related data analysis. In this talk we review four related examples. The first example involves the comparison of two event time distributions for the time until resolution of air leaks after lung surgery. The second example is about inference for dynamic treatment regimes. Another example is a Bayesian basket trial design with a nonparametric Bayesian survival regression to find benefiting subpopulations. A last example is about the construction of a synthetic control arm to supplement a single-arm trial using real world data.

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Date/Time : 07 Oct 2021 16:00
Venue : via Zoom
Speaker : Xavier Fernández-Real, EPFL

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https://nus-sg.zoom.us/j/86013696968?pwd=VHJFQkVhVmg5N0Urdk0yV3A2MEJQQT09

Meeting ID: 860 1369 6968
Passcode: 328086

Abstract:  The fractional or thin one-phase problem is the study of minimizers of the functional
J_s(u) = [u]_{H^s(B_1)}^2 + |{u > 0} \cap B_1|.
The aim of this talk is to study homogeneous stable solutions to the fractional one-phase free boundary problem. The problem of classifying stable (or minimal) homogeneous solutions in dimensions n ≥ 3 is completely open. In this context, axially symmetric solutions are expected to play the same role as Simons’ cone in the classical theory of minimal surfaces, but even in this simpler case the problem is open.

The goal of this talk is twofold and is based on a recent work with X. Ros-Oton. On the one hand, we present our first main contribution: the stability condition for the thin one-phase problem. Quite surprisingly, this requires the use of “large solutions” for the fractional Laplacian, which blow up on the free boundary. On the other hand, using our new stability condition, we show that any axially symmetric homogeneous stable solution in dimensions n ≤ 5 is one-dimensional, independently of the parameter s∈(0,1).

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Date/Time : 06 Oct 2021 15:00
Venue : via Zoom
Speaker : Jan Frahm, Aarhus University

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https://nus-sg.zoom.us/j/81603760900?pwd=d0lGRktVY0hJSTM5ODBCWmZmTVRrUT09

Meeting ID: 816 0376 0900
Passcode: 883638

Abstract:  ranching problems ask for the behaviour of the restriction of an irreducible representation of a group $G$ to a subgroup $H$. In the context of smooth representations of real reductive groups, this typically leads to the study of multiplicities with which an irreducible representation of $H$ occurs as a quotient of an irreducible representation of $G$. Here, both quantitative results such as multiplicity-one theorems and qualitative results such as the Gan-Gross-Prasad conjectures are of interest. In the context of unitary representations of real reductive groups, one can go a step further and explicitly decompose in irreducible representation of $G$ into a direct integral of irreducible representations of $H$. I will explain how branching laws for unitary representations are related to those in the smooth category, and how one can use an analytic continuation procedure along a principal series parameter to obtain explicit branching laws from certain Plancherel formulas for homogeneous spaces.

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Date/Time : 06 Oct 2021 16:00
Venue : via Zoom
Speaker : Chong Chi Tat, National University of Singapore

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https://nus-sg.zoom.us/j/83049258042?pwd=UWViaWNvTFUrdFdhOHJCdEVydnVkdz09

Meeting ID: 830 4925 8042
Passcode: 1729=x3+y3

Abstract:   In this talk we discuss the proof-theoretic strength, from the reverse mathematics perspective, of combinatorial principles concerning the coloring of binary trees and finite products of binary trees.  Beginning with the principle TT^1, which states that every finite coloring of the full binary tree has an isomorphic monochromatic subtree, we will cover its strengthening to the existence of a strong monochromatic subtree, and to the full generalization of the latter known as the Halpern-Laeuchli Theorem.

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Date/Time : 06 Oct 2021 16:00
Venue : via Zoom
Speaker : Purvi Gupta, Indian Institute of Science, Bangalore

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https://nus-sg.zoom.us/j/87511476637?pwd=VURaUDVzaHpMYmduN2Fod0h0Y29sQT09

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract: A compact subset of $\mathbb{C^n}$ is said to be polynomially convex if it is defined by a family of polynomial inequalities. Polynomial convexity grants certain approximation-theoretic properties to the underlying set. When the set is a real submanifold of $\mathbb{C^n}$, its convexity properties are partly influenced by its topology, and the local and global structure of its CR (complex-real) singularities. The minimum complex dimension into which all compact real manifolds of a fixed dimension admit smooth polynomially convex embeddings is not known (although there are some obvious bounds). In this talk, we will discuss some recent improvements on the previously known bounds, especially focusing on the odd-dimensional case, where the embeddings cannot be produced by classical (local) perturbation techniques. This is joint work with R. Shafikov.

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Date/Time : 01 Oct 2021 10:00
Venue : via Zoom
Speaker : Li Cheng, University of Alberta

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https://nus-sg.zoom.us/j/9775606531?pwd=cVZ6eTRYS3ZzVUlFNXRuSlhMVjJSUT09

Meeting ID: 977 560 6531
Passcode: 123321

Abstract:  Recent advancement of visual behavior analysis has opened door to many interesting applications. In this talk, I will discuss our research efforts toward addressing the related tasks of 3-D pose and shape estimation, action quality assessment, and motion synthesis of humans and beyond, from images and videos. Looking forward, our results could be applied to everyday life scenarios such as natural user interface, AR/VR, robotics, and gaming, among others.

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Date/Time : 30 Sep 2021 10:00
Venue : via Zoom
Speaker : Brian Collier, University of California Riverside

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https://nus-sg.zoom.us/j/87511476637?pwd=VURaUDVzaHpMYmduN2Fod0h0Y29sQT09

Meeting ID: 875 1147 6637
Passcode: 468399

Abstract:  In this talk, we will define a special class of nilpotent elements of complex semisimple Lie algebra and describe how a Slodowy slice construction defines connected components of moduli spaces of G-Higgs bundles on a compact Riemann surface for specific real groups G. Through the nonabelian Hodge correspondence, these components define connected components of the G-character variety with many nice features. We will then describe how these nice features, together with recent work of Guichard-Labourie-Wienhard on positive representations imply that such components are higher Teichmuller spaces, that is, they consist entirely of discrete and faithful representations. In the remaining time, we will describe what remains to be proven to finish the classification of higher Teichmuller spaces.

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Date/Time : 29 Sep 2021 14:00
Venue : via Zoom
Speaker : Shunsuke Yamana, Osaka City University

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https://nus-sg.zoom.us/j/86263979122?pwd=WXNuYUdnNXdhQkNOODJJNlB3MnRhQT09

Meeting ID: 862 6397 9122
Passcode: 630599

Abstract:  p-adic L-functions involve modified p-factors which measure the discrepancy between the p-adic and complex L-values in the interpolation formula. It is a puzzling fact that this factor can vanish at the central point. Then the p-adic L-function trivially vanish at the point, and such a zero is called an exceptional zero. The p-adic L-function of an elliptic curve has an exceptional zero if and only if it has split multiplicative reduction at p, and the precise relation between derivative of the p-adic L-function and the algebraic part of the complex L-value was conjectured by Mazur-Tate-Teitelbaum and proved by Greenberg-Stevens. 　 There have been many attempts to extend this result of Greenberg-Stevens to more general automorphic forms.

In this talk I will consider the exceptional zeros of the cyclotomic twisted triple product p-adic L-function associated to elliptic curves over rationals and a real quadratic field, and prove an identity between derivatives of the p-adic L-function and complex L-values. I will also consider exceptional zeros of a certain p-adic L-function of degree 6 associated with two rational elliptic curves.

This is a joint work with Ming-Lun Hsieh.

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