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 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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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 : 13 Sep 2023 14:00
Venue : S17 #05-11 (SR5)
Speaker : Jan Dobrowolski, University of Manchester

We study the relation R of collinearity of triples of points on a smooth cubic surface X. Our aim is to understand sequences of triples (A,B,C) of finite sets with |A|=|B|=|C| whose Cartesian products have asymptotically maximal possible size of intersection with the relation R (i.e. growing roughly as quickly as the square of the size of the sets A,B,C). This is an instance of the so-called Elekes-Szabó problem, which is closely related to the sum-product phenomenon. It is well-known that such configurations can be built on planar cubic curves, hence we can find them in an intersection of X with a plane. We prove this is essentially the only way in which such configurations on X arise, i.e. every such configuration on X concentrates on its intersection with a plane.

This is a joint work with Martin Bays and Tingxiang Zou.

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Date/Time : 13 Sep 2023 15:00
Venue : S17 #04-06 (SR1)
Speaker : Shuichiro Takeda, Osaka University

Let X=H\G be a symmetric variety over a p-adic field, where we assume G is split. In this talk, I will introduce a complex group G_X^\vee, which naturally gives rise to a map from G_X^\vee\time SL_2 to the Langlands dual group G^\vee. Further, I will talk about how this map is related to H-distinguished representations of G through numerous examples, especially in relation to the theory of Kato-Takano on H-relative matrix coefficients.

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Date/Time : 13 Sep 2023 16:30
Venue : S17 #04-06 (SR1)
Speaker : Arghya Sadhukhan, National University of Singapore

First introduced by Rapoport, affine Deligne-Lusztig varieties are analogues of Deligne-Lusztig varieties in the context of an affine root system. Understanding their geometry has been crucial in studying reduction of Shimura varieties and have found applications in the Langlands program; for example, description of their irreducible components has been employed to understand cycles on the special fiber a la Xiao-Zhu, whereas knowledge about their connected component has been useful in Kisin’s proof of the Langlands-Rapoport conjecture (in the hyperspecial level). In this talk, we will discuss a dimension formula for certain union of affine Deligne-Lusztig varieties of parahoric level in the case of a quasi-split group, as well as some partial results in the non-quasi split case, obtained from utilizing certain combinatorial tools arising from quantum Schubert calculus.

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Date/Time : 12 Sep 2023 10:00 - 12:00
Venue : I4-01-03 (Innovation 4.0 Building)
Speaker : Jean Bernard Lasserre, Laboratory for Analysis and Architecture of Systems

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Date/Time : 12 Sep 2023 17:00
Venue : S17 #04-06 (SR1)
Speaker : Borisa Kueljevic, University of Novi Sa

We will sketch the proof that MA(kappa) implies that each collection of P_c-points of size at most kappa which has a P_c-point as an RK upper bound also has a P_c-point as an RK lower bound.

This is joint work with Dilip Raghavan and Jonathan Verner.

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