Date/Time : 05 Oct 2023 15:30
Venue : S17 #04-06 (SR1)
Speaker : Zhe Sun, University of Science and Technology of China

Fock and Goncharov introduced a pair of mirror moduli spaces associated to G and G^L which generalized the Teichmüller space and the decorated Teichmüller space, and they proposed a duality: the canonical basis of the regular function ring of one space X is parameterized by the tropical integral points of its mirror X^V. In this talk, I will explain my joint work with Linhui Shen and Daping Weng for SL3, where we introduce the topological asymmetric intersection numbers between webs on the surfaces to provide the duality pairings and the map from webs to tropical points. We prove that the map is the same as the previous one obtained by Douglas and myself. We relate the cluster algebra and skein algebra by this intersection number and prove the mutation equivariance, where the flip equivariance is a consequence.

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Date/Time : 04 Oct 2023 14:30
Venue : S17 #05-11 (SR5)
Speaker : Shiwu Yang, Peking University

It has been shown that general large solutions to the Cauchy problem for the Maxwell-Klein-Gordon system (MKG) in the Minkowski space decay like linear solutions. One hence can define the associated radiation field on the future null infinity. In this talk, we show the existence of a global solution to the MKG system which scatters to any given sufficiently localized radiation field with arbitrarily large size and total charge. The result follows by studying the characteristic initial value problem to the MKG system with general large data by using gauge invariant vector field method. This is based on joint work with W. Dai, H. Mei and D. Wei.

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Date/Time : 04 Oct 2023 13:00
Venue : via Zoom
Speaker : Shengtong Zhang, Stanford University

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

Meeting ID: 810 4646 2775
Passcode: 23571113

In this talk, we start with Nikiforov’s spectral version of Turan’s theorem. This leads us to an intriguing conjecture of Bollobas and Nikiforov on the first two eigenvalues of graphs. Despite its simple appearance, the conjecture has resisted attacks for over 15 years. We survey several partial results on this conjecture, up to some recent progress by the speaker confirming the conjecture in the case of regular graphs. Based on https://arxiv.org/abs/2309.08184.

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Date/Time : 04 Oct 2023 16:00
Venue : S17 #04-06 (SR1)
Speaker : Wilderich Tuschmann, Karlsruhe Institute of Technology

Consider a smooth manifold with a Riemannian metric satisfying some sort of geometric constraint like, for example, positive scalar curvature, non-negative Ricci or negative sectional curvature, being Einstein, Kähler, Sasakian, etc. A natural question to ponder is then what the space of all such metrics does look like. Moreover, one can also study this question for the corresponding moduli spaces of metrics, i.e., quotients of the former by the diffeomorphism group of the manifold, acting by pulling back metrics. These spaces are customarily equipped with the topology of smooth convergence on compact subsets and the quotient topology, respectively, and their topological properties then provide the right means to measure ‘how many’ different metrics and geometries the given manifold actually does exhibit.

In my talk, I will provide a short introduction to the subject with a focus on lower curvature bounds and then discuss non-traditional approaches to these objects via Gromov-Hausdorff convergence techniques which, in particular, also allow for the study of natural compactifications. Moreover, I will describe the moduli spaces of flat metrics on closed manifolds in a new way via symmetric spaces and, if time permits, also discuss some potential applications arising from this.

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Date/Time : 21 Sep 2023 15:30
Venue : S17 #04-06 (SR1)
Speaker : Tan Ser Peow, National University of Singapore

The congruence subgroup Gamma_0(N) is the subgroup of the modular group PSL(2,Z) where the lower left-hand entry is congruent to 0 mod N. By a theorem of Kurosh, since PSL(2,Z) is freely generated by an element of order 2 and an element of order 3, any finite index subgroup of PSL(2,Z) can be freely generated by elements of order 2,3 and infinity, including Gamma_0(N).

Kulkarni used an algebraic-geometric method to give an algorithm for finding these generators, and he observed that when N is a prime less than 100, these generators can be chosen so that the lower left-hand entry is either N or 0. He conjectured that this is true for all primes. We call such a generating set an optimal generating system and we will discuss in this talk how to prove Kulkarni’s conjecture, with extensions to cases where N is the square of a prime. This is joint work with Nhat Minh Doan, Sanghyun Kim and Mong Lung Lang.

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Date/Time : 20 Sep 2023 15:00
Venue : S16 #04-35
Speaker : Goh Jun Le, National University of Singapore

We apply and reframe statements about graph decompositions, Latin squares, affine planes, etc. to statements about reductions between problems. In particular, we exhibit a statement (depending on n) which is equivalent to the existence of a finite affine plane of order n (open for many n). I expect this talk to be accessible to undergraduates.

Joint work with David Belanger and Damir Dzhafarov.

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Date/Time : 19 Sep 2023 17:00
Venue : S17 #04-06 (SR1)
Speaker : Neoh Tzeh Yuan,

The Boolean satisfiabilty problem (SAT) is a problem with great theoretical and practical interest. While heuristic algorithms tend to work well in practice, the widely believed strong exponential time hypothesis (SETH) conjectures that there is no deterministic algorithm for SAT in time O(c^n) for some constant c < 2. On the other hand, better bounds of O(c^n) with c < 2 have been found for various restricted (but still NP-complete) instances of SAT. One such problem is 3-Occur-SAT, where every variable in the formula occurs at most 3 times. Wahlstroem presented in 2005 an algorithm which solves the problem in time O(1.1279^n) and Peng and Xiao improved it (this year’s IJCAI) to O(1.1238^n).

I will present an algorithm that gives a further improvement to O(1.1199^n). I’ll discuss the common bottleneck cases faced by previous efforts and introduce new reduction and branching rules that can circumvent these cases.

The work I present is done in an internship at NUS / SOC supervised by Sanjay Jain and Frank Stephan from July to September 2023.

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Date/Time : 14 Sep 2023 17:00
Venue : S17 #04-06 (SR1)
Speaker : Jan Dobrowolski, University of Manchester

The class of NSOP1 theories, originally introduced by Dzamonja and Shelah in 2004, has been studied very intensively in the last few years since the striking discovery of an independence relation called Kim-independence by Ramsey and Kaplan (based on earlier ideas of Kim and a work of Chernikov and Ramsey), which generalises forking independence in simple theories, and retains almost all its nice properties in the class of NSOP1 theories.

I will start the talk with an overview of the notion of Kim-independence, and then I will present my joint work with Mark Kamsma on generalising Kim-independence to positive logic. In particular, I will discuss examples of positive NSOP1 theories falling into our framework such as the theory of existentially closed exponential fields (studied by Kirby and Haykazyan), the theory of fields with a generic submodule (studied by d’Elbee, Kaplan and Neuhauser) and the hyperimaginary extensions of NSOP1 theories.

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Date/Time : 14 Sep 2023 15:30
Venue : S17 #05-11 (SR5)
Speaker : Daniel Huson, University of Tubingen

This talk has four parts. In the first part – topology -, we recall the classification of two-dimensional manifolds and orbifolds, and introduce their Conway-Macbeath notation. In the second part – geometry -, we discuss two-dimensional periodic tilings and their classification. In the third part – combinatorics -, we introduce Delaney-Dress symbols and indicate how they can be used to systematically enumerate periodic tilings. Finally, in the fourth part – algorithms and software -, we present Tegula

(https://ddec1-0-en-ctp.trendmicro.com:443/wis/clicktime/v1/query?url=http%3a%2f%2ftegula.husonlab.org&umid=7c8bc7cd-aafa-4ab0-9fe7-ed56d83a50f7&auth=8d3ccd473d52f326e51c0f75cb32c9541898e5d5-113b232b1017a668b66ec7edf1b8b0f54e074fb4),

a new computer program that can be used the explore the “galaxy” of all 2.4 billion periodic tilings of the euclidean plane, sphere and hyperbolic plane, of low Dress-complexity. This is joint work with Olaf Delgado and Rüdiger Zeller.

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