Date/Time : 22 Jan 2020 17:00
Venue : S17 #04-06 SR1
Speaker : Asger Dag Toernquist, Kobenhavns Universitet

Date/Time:22 Jan 2020 17:00 Venue: S17 #04-06 SR1 Speaker: Asger Dag Toernquist, Kobenhavns Universitet Mad, med, mcg and other maximal combinatorial objects This talk is about the descriptive set theory and infinitary combinatorics. In the past 6 years, a number of long-standing problems related to the definability (in the sense of effective descriptive set theory) of so-called maximal almost disjoint (mad) families, maximal eventually different (med) families, and maximal cofinitary groups (mcg) have been solved by an array of authors. I will give an overview of these developments. Almost disjoint families are families of infinite subsets of omega where any two distinct elements of the family intersect finitely; eventually different families are families of functions from omega to omega such that any two distinct functions in the family are eventually different; and cofinitary groups are subgroups of the group of all permutations of omega with the property that all non-identity elements of the group have at most finitely many fixed points. Maximality of such objects in all cases means maximal under inclusion (among such families). A classical result due to Adrian Mathias states that no analytic infinite mad families. A slew of recent results shed light on this classical result by showing that under suitable descriptive set-theoretic regularity assumptions, there are no mad families at all (and this localizes to suitable pointclasses, especially to analytic sets). In a totally unexpected twist, Horowitz and Shelah showed in 2016 that there are Borel med families and mcg, solving a long-standing problem. I will finish the talk by discussing some related, still unsolved problems, especially the following: Is there a maximal (infinite) analytic set of pairwise Turing-incomparable reals? Add to calendar: 

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Date/Time : 15 Jan 2020 17:00
Venue : S17 #04-06 SR1
Speaker : Frank Stephan, National University of Singapore

Date/Time:15 Jan 2020 17:00 Venue: S17 #04-06 SR1 Speaker: Frank Stephan, National University of Singapore Measure and Conquer for Max Hamming Distance XSAT This talk gives an overview of the joint work of the speaker’s ecent work on the Hamming XSAT problem. This problem asks for an algorithm to determine which, given an XSAT instance, determines the maximum Hamming distance between two solutions of this instance. The problem has been studied by Dahloef in 2005 in an ISAAC paper who provided an O(1.83848^n) algorithm for this problem. Later Fu, Zhu and Yin presented at JFCST 2012 an O(1.6760^n) algorithm for the related Max Hamming X3SAT problem where all clauses have at most three literals. The current paper provides for the general Max Hamming XSAT problem an O(1.4983^n) algorithm which applies also the technique “Measure and Conquer” in order to prove a better bound than the algorithm would give otherwise. Furthermore, the algorithm does not only provide the maximum Hamming distance of two solutions of the instance, but instead for each k between 0 and n the number of pairs of solutions which have Hamming distance k. For the special case Max Hamming Distant X3SAT, Hoi, Jain and Stephan have the bound O(1.3298^n) at the conference FSTTCS 2019. Add to calendar: 

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Date/Time : 02 Dec 2019 17:00
Venue : S17 #06-11
Speaker : Rupert Hoelzl, University of the Bundeswehr, Munich

Date/Time:02 Dec 2019 17:00 Venue: S17 #06-11 Speaker: Rupert Hoelzl, University of the Bundeswehr, Munich Randomness for computable measures and complexity We study the possible growth rates of the Kolmogorov complexity of initial segments of sequences that are random with respect to some computable measure on the Cantor Space, the so-called proper sequences. Our main results are as follows: (1) We show that the initial segment complexity of a proper sequence X is bounded from below by a computable function (that is, X is complex) if and only if X is random with respect to some computable, continuous measure. (2) We prove that a uniform version of the previous result fails to hold: there is a family of complex sequences that are random with respect to a single computable measure such that for every computable, continuous measure mu, some sequence in this family fails to be random with respect to mu. (3) We show that there are proper sequences with extremely slow-growing initial segment complexity, that is, there is a proper sequence the initial segment complexity of which is infinitely often below every computable function, and even a proper sequence the initial segment complexity of which is dominated by all computable functions. (4) We prove various facts about the Turing degrees of such sequences and show that they are useful in the study of certain classes of pathological measures on the Cantor Space, namely diminutive measures and trivial measures. Add to calendar: 

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Date/Time : 14 Nov 2019 17:00
Venue : S17 #06-11
Speaker : Thilo Weinert, National University of Singapore

Date/Time:14 Nov 2019 17:00 Venue: S17 #06-11 Speaker: Thilo Weinert, National University of Singapore Partition Relations for Linear Orders in a Choiceless Context Most Partition Relations are proved for Ordinals, not general linear orders. This is due to the Axiom of Choice which I will consequently ignore during most of the lecture. Some exceptions to the rule mentioned at the beginning can be found in a 1971 paper by Erdoes, Milner and Rado and I will present some analogous results for linear orders which are given rise to by lexicographically ordered sequences of zeros and ones. I will close by discussing an open problem in this context. This is joint work (from a few years back) with Philipp Luecke and Philipp Schlicht. Add to calendar: 

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Date/Time : 07 Nov 2019 17:00
Venue : S17 #06-11
Speaker : Chong Chi Tat, National University of Singapore

Date/Time:07 Mar 2019 16:00 Venue: S17 #05-12 SR4 Speaker: Wu Bin On Large Games with Bio-social Traits This paper shows that, in a class of large games with traits model, distinguishing agent space and trait space via the nowhere equivalence condition is not only sufficient but also necessary for the existence of pure strategy Nash equilibrium and closed graph property. Furthermore, under the nowhere equivalence condition, we characterize Nash equilibria of large games with traits. Add to calendar: 

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Date/Time : 31 Oct 2019 17:00
Venue : S17 #06-11
Speaker : Marat Arslanov, Kazan Federal University

Date/Time:31 Oct 2019 17:00 Venue: S17 #06-11 Speaker: Marat Arslanov, Kazan Federal University n-c.e. degrees, CEA operators and fixed-point selection functions The subjects listed in the title of my talk belong to my steady scientific interest. In my talk I will speak about my recent work in these areas and list few open problems that have arisen as a result of these studies and that I can’t answer. Note: The originally planned talk by Wu Guohua for that day will be moved to the next semester. Apologies for the short notice change. Add to calendar: 

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Date/Time : 24 Oct 2019 17:00
Venue : S17 #06-11
Speaker : Yang Yue, National University of Singapore

Date/Time:24 Oct 2019 17:00 Venue: S17 #06-11 Speaker: Yang Yue, National University of Singapore Ramsey’s Theorem on trees and weak Koenig’s Lemma Ramsey’s Theorem for Pairs has been studied intensively in reverse mathematics. One of the major breakthroughs is Liu Lu’s 2012 result showing RT-2-2 does not imply WKL-0. Liu’s result not only answered an important question in reverse mathematics, the technique that he used turns out to have wider applications, for example, in Monin and Patey’s separation of SRT-2-2 and RT-2-2. In this talk, we generalize Liu’s result to tree. Let TT-2-k denote the combinatorial principle stating that every k-coloring of pairs of compatible nodes on the full binary tree has a homogeneous solution, i.e. an infinite perfect tree in which all pairs of compatible nodes have the same color. We show that over the base system RCA-0, TT-2-k doe not imply weak Koenig’s lemma. This is joint work with Chong Chitat, Li Wei and Liu Lu. Add to calendar: 

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Date/Time : 17 Oct 2019 17:00
Venue : S17 #06-11
Speaker : Li Zeyong,

Date/Time:17 Oct 2019 17:00 Venue: S17 #06-11 Speaker: Li Zeyong A Complete Problem for Statistical Zero Knowledge This work by Amit Sahai and Salil Vadhan presents the first complete problem for SZK, the class of promise problems possessing statistical zero-knowledge proofs (against an honest verifier). The problem, called STATISTICAL DIFFERENCE, is to decide whether two efficiently samplable distributions are either statistically close or far apart. This gives a new characterization of SZK that makes no reference to interaction or zero knowledge. The talk (due to time constraint) will focus on the second half (and arguably the more insightful half) of the completeness theorem, that is, STATISTICAL DIFFERENCE is SZK-hard. It essentially gives a constructive proof that any promise problem possessing a statistical zero-knowledge proof can be reduced to an instance of STATISTICAL DIFFERENCE in polynomial time. Add to calendar: 

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Date/Time : 10 Oct 2019 17:00
Venue : S17 #06-11
Speaker : Ashutosh Kumar, National University of Singapore

Date/Time:10 Oct 2019 17:00 Venue: S17 #06-11 Speaker: Ashutosh Kumar, National University of Singapore On partitions into null sets Given a partition P of the set of reals into Lebesgue null sets, let J be the ideal of those subsets of P whose union is null. We’ll show that, consistently, J can be countably saturated. This is a joint work with Saharon Shelah. Add to calendar: 

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