Date/Time : 10 Aug 2022 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Yifan Jing, University of Oxford

Abstract:  Given natural numbers $s$ and $k$, we say that a finite set $X$ of integers is an additive $B_{s}[k]$ set if for any integer $n$, the number of solutions to the equation \[ n = x_1 + … + x_s, \] with $x_1, …, x_s$ lying in $X$, is at most $k$, where we consider two such solutions to be the same if they differ only in the ordering of the summands. We define a multiplicative $B_{s}[k]$ set analogously. These sets have been studied thoroughly from various different perspectives in combinatorial and additive number theory. In this talk, we will discuss sum-product phenomena for these sets. We show that there is either an exceptionally large additive $B_{s}[k]$ set, or an exceptionally large multiplicative $B_{s}[k]$ set, with $k \ll s$. This is joint work with Akshat Mudgal.

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Date/Time : 10 Aug 2022 17:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Tran Chieu-Minh, National University of Singapore

Abstract:  For a bivariate P(x,y) in R[x,y] – (R[x] union R[y]), we show that for all finite subsets A of R,|P(A,A)| is greater or equal alpha |A|^(5/4) with alpha = alpha(deg P) being a real number greater than 0, P(x,y)=f(gamma u(x)+delta u(y)) or P(x,y)=f(u^m(x)u^n(y)) for some univariate f, u R[t] – </b>, constants gamma, delta in R – {0}</b> and m, n in {1,2,3,…}.

This resolves the symmetric nonexpanders classification problem proposed by de Zeeuw and is a step towards the analog for polynomials of the Erdoes-Szemeredi sumproduct Conjecture. The proofs of our results use tools from semialgebraic / o-minimal geometry.

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Date/Time : 27 Jul 2022 14:00
Venue : S17 #04-04 (SR3)
Speaker : Paolo Cascini, Imperial college

Abstract:  I will survey some recent results on the study of the birational geometry of foliations over complex projective varieties, focusing, in particular, on the case of algebraically integrable foliations.

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Date/Time : 26 Jul 2022 15:00
Venue : S17 #04-06 (SR1)
Speaker : Antonio De Rosa, University of Maryland

Abstract: We prove the existence of nontrivial closed surfaces with constant anisotropic mean curvature with respect to elliptic integrands in closed smooth 3-dimensional Riemannian manifolds. The constructed min-max surfaces are smooth with at most one singular point. The constant anisotropic mean curvature can be fixed to be any real number. In particular, we partially solve a conjecture of Allard [Invent. Math.,1983] in dimension 3. Joint work with Guido De Philippis.

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Date/Time : 26 Jul 2022 16:00
Venue : via Zoom
Speaker : Piyush Srivastava, Tata Institute of Fundamental Research

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https://nus-sg.zoom.us/j/83199111482?pwd=L09Yd054dDNTbDBpRkNtc0tmQnk5Zz09

Meeting ID: 831 9911 1482
Passcode: 569991

This series of lectures will survey various applications to algorithms of a collection of techniques that are broadly referred to as “geometry of polynomials”. Specific examples include:

1) Real stable polynomials and constructions of Ramanujan expanders
2) Lee-Yang theory and deterministic “approximate counting” algorithms”
3) Lorentzian or “strongly log concave” polynomials and applications to sampling.

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Date/Time : 19 Jul 2022 16:00
Venue : via Zoom
Speaker : Piyush Srivastava, Tata Institute of Fundamental Research

Join Zoom Meeting
https://nus-sg.zoom.us/j/83199111482?pwd=L09Yd054dDNTbDBpRkNtc0tmQnk5Zz09

Meeting ID: 831 9911 1482
Passcode: 569991

This series of lectures will survey various applications to algorithms of a collection of techniques that are broadly referred to as “geometry of polynomials”. Specific examples include:

1) Real stable polynomials and constructions of Ramanujan expanders
2) Lee-Yang theory and deterministic “approximate counting” algorithms”
3) Lorentzian or “strongly log concave” polynomials and applications to sampling.

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Date/Time : 15 Jul 2022 16:00
Venue : S17 #04-04 (SR3)
Speaker : Defeng Sun, The Hong Kong Polytechnic University

Abstract: It has been widely recognized that the structured sparsity of the optimal solutions is an intrinsic property for large-scale optimization problems arising from modern applications in the big data era. In this talk, we shall first illustrate the structured sparsity of the solutions via some popular machine learning models. In particular, we shall show that the solution of the convex clustering model can be highly structurally sparse even if the solution itself is fully dense. We shall then introduce a dual semismooth Newton based proximal point algorithm (PPDNA) and explain why it can be much more efficient than the first-order methods for solving a class of large-scale optimization problems arising from machine learning. The key point is to adaptively make use of the second-order sparsity of the solutions in addition to the data sparsity so that, at each iteration, the computational costs of the second-order methods can be comparable or even lower than those of the first-order methods. Equipped with the PPDNA, we shall then introduce some adaptive sieving methodologies to generate solution paths for large-scale optimization problems with structured sparsity of particular importance in applications. In the last part of the talk, we shall illustrate the high efficiency of our approach with extensive numerical results on several important models including convex clustering, lasso, and exclusive lasso.

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Date/Time : 12 Jul 2022 16:00
Venue : via Zoom
Speaker : Piyush Srivastava, Tata Institute of Fundamental Research

Join Zoom Meeting
https://nus-sg.zoom.us/j/83199111482?pwd=L09Yd054dDNTbDBpRkNtc0tmQnk5Zz09

Meeting ID: 831 9911 1482
Passcode: 569991

This series of lectures will survey various applications to algorithms of a collection of techniques that are broadly referred to as “geometry of polynomials”. Specific examples include:

1) Real stable polynomials and constructions of Ramanujan expanders
2) Lee-Yang theory and deterministic “approximate counting” algorithms”
3) Lorentzian or “strongly log concave” polynomials and applications to sampling.

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Date/Time : 04 Jul 2022 16:00
Venue : S17 #06-11 (SR6)
Speaker : Sang-hyun Kim, Korea Institute of Advanced Study

Abstract:  We prove that for each finite index subgroup H of the mapping class group of a closed hyperbolic surface, and for each real number r>1 there does not exist a faithful C^r-action (in Hölder’s sense) of H on a circle. For this, we partially determine the optimal regularity of faithful actions by right-angled Artin groups on a circle. (Joint with Thomas Koberda and Cristobal Rivas).

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