Date/Time : 14 Nov 2023 17:00
Venue : S17 #04-06 (SR1)
Speaker : Liu Shixiao,

Last semester I talked about the upper density Mathias forcing which we prove to be proper. This time we take a look at several similar forcings, each of which collapses the continuum to omega and thus fails to be proper.

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Date/Time : 09 Nov 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Zhang Mengqi, National University of Singapore

Recent studies revealed that viscoelastic (polymeric) pipe flows can be linearly unstable, in contrast to the stability of the Newtonian pipe flows. The new linear instability was found to be a center mode with the eigenfunction concentrating in the center part of the pipe (Garg et al. 2018). We carried out linear stability analysis and transient energy growth analysis to further explore the linear dynamics of the center mode. It is found that an Orr mechanism(along with the critical-layer mechanism) is at play in the conformation tensor field, contributing to the total energy growth.

From a nonlinear point of view, the linear instability implies a possibility of supercritical bifurcation in viscoelastic pipe flows, again, in contrast to the subcritical Newtonian pipe flows. We applied a multiple-scale expansion method to study the bifurcation of the viscoelastic pipe flows. It is found that both supercritical and subcritical bifurcations exist in this flow. We calculated the boundary between the two bifurcations in terms of viscosity ratio (related to the polymer concentration) and our theoretical prediction gave a value about 0.785 (below which, the flow is supercritical; vice versa),qualitatively close to the experimental observation around 0.855. A scaling for the Landau coefficient has also been found.

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Date/Time : 09 Nov 2023 16:00
Venue : S17 #06-11 (SR6)
Speaker : Andreas Wieser, Hebrew University of Jerusalem

In the 80’s, Livingston asked whether there exist Seifert surfaces F,F’ for the same knot so that, after pushing their interiors into the four-ball, the surfaces are not topologically ambient isotopic. The question has recently been resolved by Hayden, Miller, Kim, Park, and Sundberg whose example satisfies that the interiors of the surfaces are disjoint. In joint work with Menny Aka, Peter Feller, and Alison B. Miller we classify all examples that can be recognized algebraically. This is based on an exact number-theoretic characterization of pairs of Seifert forms that can arise from Seifert surfaces with disjoint interiors. Here, the characterization is in terms of the Gauss composition of binary quadratic forms. In the second half of the talk we will also discuss asymptotic independence questions related to the above setting (based on work with Aka and Einsiedler) as well as open questions. No preliminaries are assumed. The first half of the talk will be focused on geometry and the second will be number-theoretical in nature (bordering on homogeneous dynamics).

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Date/Time : 08 Nov 2023 14:00
Venue : S17 #05-11 (SR5)
Speaker : Xiaoqian Xu, Duke Kunshan University

In the study of incompressible fluid, one fundamental phenomenon that arises in a wide variety of application is dissipation enhancement by so-called mixing flow. In this talk, I will give a brief introduction to the idea of mixing flow and the role it plays in the field of advection-diffusion-reaction equation, such as the famous Keller-Segel equation for chemotaxis. I will also discuss about the examples of such flows in this talk.

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Date/Time : 07 Nov 2023 17:00
Venue : S17 #04-06 (SR1)
Speaker : Ye Jinhe , University of Oxford

A difference field is a field equipped with a given automorphism and a difference variety is the natural analogue of an algebraic varieties in this setting. Complex numbers with complex conjugation or finite fields with the Frobenius automorphism are natural examples of difference fields.

For finite fields and varieties over them, the celebrated Lang-Weil estimate gives a universal estimate of number of rational points of varieties over finite fields in terms of several notions of the complexities of the given variety. In this talk, we will discuss an analogue to Lang-Weil estimate for difference varieties in finite difference fields. The proof uses pseudofinite difference fields, where the automorphism is the nonstandard Frobenius. This is joint work with Martin Hils, Ehud Hrushovski and Tingxiang Zou.

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Date/Time : 01 Nov 2023 16:30
Venue : S17 #05-11 (SR5)
Speaker : Lin Ting, Peking University

In this talk, I will introduce the construction of the $C^r$ finite element space in any dimension. We show that $C^r$ finite element in $\mathbb R^d$ can be constructed, with the local shape function space $\mathcal P_{k}$ ($k\ge 2^d r+1$). Moreover, we show that the assumptions in our construction are sharp. This is based on joint work with Jun Hu (PKU), Qingyu Wu (PKU), and Beihui Yuan (YMSC).

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Date/Time : 31 Oct 2023 17:00
Venue : S17 #04-06 (SR1)
Speaker : Samuel Alfaro Tanuwijaya, National University of Singapore

The talk will deal with relativised versions of the Posner Robinson theorem and explore how far one can go and how to prove these relatived versions.

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Date/Time : 30 Oct 2023 14:00
Venue : S17 #04-06 (SR1)
Speaker : David Chew, NUS, Statistics & Data Science

In this talk, I will describe the effort at the Department of Statistics and Data Science to offer more courses in the Blended Learning (BL) format.

Here are some aspects of the general strategy adopted by the department:
1. Replace one of the two weekly lecture meetings by pre-recorded videos that give high level overviews of topics covered.
2. Hold in-person lectures once a week; dive deeper into the materials by going through proofs, computational applications and/or in-depth examples.
3. In all our gateway classes, senior students are hired as student helpers (SHs) to provide extra support to students. SHs are each assigned 12 ~ 15 students, to answer queries, provide consultation/coding help during (and outside of) lecture and tutorial hours.

As for the tool used for making videos, the department recommends the use of Descript, an all-in-one audio and video editing software. It allows one to make videos using AI generated voices, so that videos are made with a “neutral” voice. This make the videos more “transferrable” — they can be (easily adapted and) used by another instructor, or in other courses.

We will also discuss other tools used by some colleagues (TeX, ImageMagick, etc) and other practical considerations when offering a course in BL format: logistics, manpower etc.

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Date/Time : 25 Oct 2023 14:00
Venue : via Zoom
Speaker : Simon Machado, ETH Zurich

Join Zoom Meeting
https://nus-sg.zoom.us/j/81046462775?pwd=aDhaYnhQOTgybzdYS21yajlQdnBmZz09

Meeting ID: 810 4646 2775
Passcode: 23571113

Abstract: The doubling constant of a subset $A$ of a group is defined as the ratio of the size of $A^2$ (the set of products of two elements of $A$) by the size of $A$. It is now well-established that the doubling constant $K$ of $A$ captures a great deal of information about the additive structure of $A$. For instance, if $K < 3/2$, then $A$ itself must be a coset of a group. The generalised Breuillard—Green conjecture asserts that, conversely, if one knows that $A$ is a subset of a compact simple Lie group, then $K$ must be bounded below by an explicit dimensional constant, and provides examples saturating this inequality.

I will discuss a proof of that conjecture assuming that $A$ is sufficiently small to begin with. This will take us through the theory of additive combinatorics and, perhaps surprisingly, some optimal transport. If time permits I will also discuss what we know about subsets whose doubling constant is near the minimal value.

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