Title   name   2019 Intensive Lectures by Yujiro Kawamata Intensive Lectures on Semi-orthogonal decomposition of a derived category of an algebraic variety IV Yujiro Kawamata (Univ. of Tokyo, Japan) 2019-01-24   I will start with the definition of a derived category of an algebraic variety. The derived category contains much essential information of the algebraic variety. Then I consider a decomposition of the derived category into simpler components called a semi-orthogonal decomposition (SOD) and explain examples. I will explain SOD’s related to the minimal model program in birational geometry. Some SOD’s are obtained by looking at so-called exceptional objects or their deformed variants called relative exceptional objects. I will explain examples of SOD’s for some singular surfaces.   2019 Intensive Lectures by Yujiro Kawamata Intensive Lectures on Semi-orthogonal decomposition of a derived category of an algebraic variety III Yujiro Kawamata (Univ. of Tokyo, Japan) 2019-01-22   I will start with the definition of a derived category of an algebraic variety. The derived category contains much essential information of the algebraic variety. Then I consider a decomposition of the derived category into simpler components called a semi-orthogonal decomposition (SOD) and explain examples. I will explain SOD’s related to the minimal model program in birational geometry. Some SOD’s are obtained by looking at so-called exceptional objects or their deformed variants called relative exceptional objects. I will explain examples of SOD’s for some singular surfaces.   2019 Intensive Lectures by Yujiro Kawamata Intensive Lectures on Semi-orthogonal decomposition of a derived category of an algebraic variety II Yujiro Kawamata (Univ. of Tokyo, Japan) 2019-01-18   I will start with the definition of a derived category of an algebraic variety. The derived category contains much essential information of the algebraic variety. Then I consider a decomposition of the derived category into simpler components called a semi-orthogonal decomposition (SOD) and explain examples. I will explain SOD’s related to the minimal model program in birational geometry. Some SOD’s are obtained by looking at so-called exceptional objects or their deformed variants called relative exceptional objects. I will explain examples of SOD’s for some singular surfaces.   2019 Intensive Lectures by Yujiro Kawamata Intensive Lectures on Semi-orthogonal decomposition of a derived category of an algebraic variety I Yujiro Kawamata (Univ. of Tokyo, Japan) 2019-01-16   I will start with the definition of a derived category of an algebraic variety. The derived category contains much essential information of the algebraic variety. Then I consider a decomposition of the derived category into simpler components called a semi-orthogonal decomposition (SOD) and explain examples. I will explain SOD’s related to the minimal model program in birational geometry. Some SOD’s are obtained by looking at so-called exceptional objects or their deformed variants called relative exceptional objects. I will explain examples of SOD’s for some singular surfaces.   2018 KAIST 세미나 Group actions in low dimensions - Part 3-1 Kathryn Mann  (Brown University) 2018-12-11   This series of lecture will introduce the study of groups acting on the circle and the line, the moduli spaces of such actions, and the role of these spaces in questions of geometric topology, dynamics, and foliation theory. I will focus on new rigidity results in low regularity, surveying important techniques, geometrically motivated examples, and open problems.   2018 KAIST 세미나 Group actions in low dimensions - Part 3-2 Kathryn Mann  (Brown University) 2018-12-11   This series of lecture will introduce the study of groups acting on the circle and the line, the moduli spaces of such actions, and the role of these spaces in questions of geometric topology, dynamics, and foliation theory. I will focus on new rigidity results in low regularity, surveying important techniques, geometrically motivated examples, and open problems.   2018 KAIST 세미나 Group actions in low dimensions - Part 2-1 Kathryn Mann  (Brown University) 2018-12-10   This series of lecture will introduce the study of groups acting on the circle and the line, the moduli spaces of such actions, and the role of these spaces in questions of geometric topology, dynamics, and foliation theory. I will focus on new rigidity results in low regularity, surveying important techniques, geometrically motivated examples, and open problems.   2018 KAIST 세미나 Group actions in low dimensions - Part 2-2 Kathryn Mann  (Brown University) 2018-12-10   This series of lecture will introduce the study of groups acting on the circle and the line, the moduli spaces of such actions, and the role of these spaces in questions of geometric topology, dynamics, and foliation theory. I will focus on new rigidity results in low regularity, surveying important techniques, geometrically motivated examples, and open problems.   2018 KAIST 세미나 Group actions in low dimensions - Part 1-1 Kathryn Mann  (Brown University) 2018-12-07   This series of lecture will introduce the study of groups acting on the circle and the line, the moduli spaces of such actions, and the role of these spaces in questions of geometric topology, dynamics, and foliation theory. I will focus on new rigidity results in low regularity, surveying important techniques, geometrically motivated examples, and open problems.   2018 KAIST 세미나 Group actions in low dimensions - Part 1-2 Kathryn Mann  (Brown University) 2018-12-07   This series of lecture will introduce the study of groups acting on the circle and the line, the moduli spaces of such actions, and the role of these spaces in questions of geometric topology, dynamics, and foliation theory. I will focus on new rigidity results in low regularity, surveying important techniques, geometrically motivated examples, and open problems.   2018 KAIST 세미나 Syzygies and Koszul modules Marian Aprodu (University of Bucharest) 2018-12-07   I will recall some basic facts in the syzygy theory, with emphasis on connections with Koszul cohomology, and I will present a vanishing result for Koszul modules.   2018 KAIST 세미나 Syzygy schemes Edoardo Sernesi (Universita Di Roma) 2018-12-07   I will introduce the syzygy schemes of a canonical curve and compute a few examples.   2018 KAIST Math. Colloquium Orderable groups in topology and dynamics Kathryn Mann  (Brown University) 2018-12-06   Given a group G and a manifold M, can one describe all the actions of G on M? This is a basic, natural question in geometric topology, but also a very difficult one -- even in the case where M is 1-dimensional, and G is a familiar, finitely generated group. This talk will introduce the theory of groups acting on 1-manifolds, through the study of orderable groups. I will describe some connections between this theory and themes in topology and dynamics (like rigidity and foliation theory ), some current open problems, and indicate new approaches coming from recent joint work with C. Rivas.   2018 Discrete Math 세미나 Largest 2-regular subgraphs in 3-regular graphs Choi, Ilkyoo (Hankuk University of Foreign Studies) 2018-11-26   For a graph G, let f2(G) denote the largest number of vertices in a 2-regular subgraph of G. We determine the minimum of f2(G) over 3-regular n-vertex simple graphs G. To do this, we prove that every 3-regular multigraph with exactly c cut-edges has a 2-regular subgraph that omits at most max{0,⎣(c-1)/2⎦} vertices. More generally, every n-vertex multigraph with maximum degree 3 and m edges has a 2-regular subgraph that omits at most max{0, ⎣(3n-2m+c-1)/2⎦} vertices. More generally, every n-vertex multigraph with maximum degree 3 and m edges has a 2-regular subgraph that omits at most max{0, ⎣(3n-2m+c-1)/2⎦} vertices.   2018 KAIST Math. Colloquium Pareto distributions in economics 김지희 (KAIST) 2018-11-22   This talk introduces one of surprising empirical regularities observed in economics: Pareto distributions are everywhere. Wealth and income, the size of cities and firms, stock market returns, to list but a few, are all known to follow a Pareto distribution. I first highlight key empirical facts and describe some economic theories that have been proposed to explain the regularity. To be more specific, I will put emphasis on inequality in income distributions. A simple mechanism as well as more complex random growth models that give rise to Pareto distributions will be discussed to explore dynamics of income inequality.   해외석학 특별강연 시리즈 Remarks on the Riemann Hypothesis Charles M. Newman  (NYU Courant) 2018-11-14   One fairly standard version of the Riemann Hypothesis (RH) is that a specific probability density on the real line has a moment generating function (Laplace transform) that, as an analytic function on the complex plane, has all its zeros pure imaginary. We'll review a series of results that span the period from the 1920's to 2018 concerning a perturbed version of the RH. In that perturbed version, due to Polya, the log of the probability density is modified by a quadratic term. This gives rise to an implicitly defined real constant known as the de Bruijn-Newman Constant, Lambda. The conjecture and now theorem (Newman 1976, Rodgers and Tao 2018) that Lambda is greater than or equal to zero is complementary to the RH which is equivalent to Lambda less than or equal to zero; The conjecture/theorem is a version of the dictum that the RH, if true, is only barely so. Until very recently, the best upper bound, was a 2009 result of Ki, Kim and Lee that Lambda is strictly less than 1/2.   2018 Discrete Math 세미나 Faster Exact and Approximate Algorithms for k-Cut  이의웅 (NYU) 2018-11-13   In the k-cut problem, we are given an edge-weighted graph G and an integer k, and have to remove a set of edges with minimum total weight so that G has at least k connected components. This problem has been studied various algorithmic perspectives including randomized algorithms, fixed-parameter tractable algorithms, and approximation algorithms. Their proofs of performance guarantees often reveal elegant structures for cuts in graphs. It has still remained an open problem to (a) improve the runtime of exact algorithms, and (b) to get better approximation algorithms. In this talk, I will give an overview on recent progresses on both exact and approximation algorithms. Our algorithms are inspired by structural similarities between k-cut and the k-clique problem.   2018 KAIST Math. Colloquium Modular forms and higher Chow cycles Ramesh Sreekantan  (Indian Statistical Institute, Bangalore) 2018-11-08   Gross and Zagier made a conjecture on the algebraicity of values of certain `higher' Greens functions at special points. Mellit proved a few cases by linking it to the existence of certain higher Chow cycles. Viazovska proved a few cases by linking it to Borcherds lifts of modular forms. We formulate a conjecture linking modular forms and higher Chow cycles which relates the two approaches and also describe a construction of higher Chow cycles which allows us to prove special cases of the Gross-Zagier conjecture as well as provide evidence for our conjecture.   2018 Discrete Math 세미나 On the rational Turán exponents conjecture 강동엽 (KAIST) 2018-11-05   The extremal number ex(n,F) of a graph F is the maximum number of edges in an n-vertex graph not containing F as a subgraph. A real number r∈[1,2] is realisable if there exists a graph F with ex(n , F) = Θ(nr). Several decades ago, Erdős and Simonovits conjectured that every rational number in [1,2] is realisable. Despite decades of effort, the only known realisable numbers are 1,7/5,2, and the numbers of the form 1+(1/m), 2-(1/m), 2-(2/m) for integers m≥1. In particular, it is not even known whether the set of all realisable numbers contains a single limit point other than two numbers 1 and 2. We discuss some recent progress on the conjecture of Erdős and Simonovits. First, we show that 2-(a/b) is realisable for any integers a,b≥1 with b>a and b≡±1 (mod a). This includes all previously known ones, and gives infinitely many limit points 2-(1/m) in the set of all realisable numbers as a consequence. Secondly, we propose a conjecture on subdivisions of bipartite graphs. Apart from being interesting on its own, we show that, somewhat surprisingly, this subdivision conjecture in fact implies that every rational number between 1 and 2 is realisable. This is joint work with Jaehoon Kim and Hong Liu.   2018 KAIST Math. Colloquium SIR Models: From Micro to Macro and Back Again Grzegorz A. Rempala  (Ohio State University) 2018-11-01   Recently, there has been considerable interest in both inference and predictions for compartmental epidemic models on multiple physical scales. For instance, one could be interested in analyzing response of immune system to infection within a single host or in describing infectuous interactions in a population of hosts. Both viral invasions and global pandemics are often described by similar mathematical constructs known as SIR models. In this talk I will review some basic concepts related to such models across scales and present a simple unifying framework that allows to conceptually connect both deterministic (e.g., population level) and stochastic (e.g., molecular level) SIR models with the help of tools of statistical theory of survival analysis.   2018 KAIST Math. Colloquium Periodic orbits in symplectic geometry 강정수 (서울대학교) 2018-10-25   Symplectic geometry has one of its origins in Hamiltonian dynamics. In the late 60s Arnold made a fundamental conjecture about the minimal number of periodic orbits of Hamiltonian vector fields. This is a far-reaching generalization of Poincaré's last geometric theorem and completely changed the field of symplectic geometry. In the last 30 years symplectic geometry has been tremendously developed due to the theory of holomorphic curves by Gromov and Floer homology theory by Floer. I will give a gentle introduction to the field of symplectic geometry and explain how modern methods give rise to existence results for periodic orbits and discover rigidity phenomena in symplectic geometry.   해외석학 특별강연 시리즈 Representation theory and geometry I  Geordie Williamson  (University of Sydney) 2018-10-23   One of the most fundamental questions in representation theory asks for a description of the simple representations. I will give an introduction to this problem with an emphasis on the representation theory of Lie groups and algebras. A recurring theme is the appearance of geometric techniques in seemingly algebraic problems. I will also emphasise the important role played by invariant forms and signature.   해외석학 특별강연 시리즈 Representation theory and geometry II Geordie Williamson  (University of Sydney) 2018-10-23   One of the most fundamental questions in representation theory asks for a description of the simple representations. I will give an introduction to this problem with an emphasis on the representation theory of Lie groups and algebras. A recurring theme is the appearance of geometric techniques in seemingly algebraic problems. I will also emphasise the important role played by invariant forms and signature.   2018 KAIST Math. Colloquium Quotients of affine spaces by finite groups: from Noether’s problem to Colliot-Thélène conjecture  Danny Neftin  (Technion) 2018-10-11   Given an action of a finite group G on an affine space A^n, the quotient variety A^n/G have been a subject of interest for over a century, partially motivated by Noether's problem concerning its rationality. Weaker properties of this variety were extensively studied, relating it to the Inverse Galois problem, parametrization of Galois extensions and essential dimension. One of its weakest possible properties, (very) weak approximation, is the subject of a more recent conjecture by Colliot-Th'el`ene. We shall discuss the above rationality properties, the conjecture, and the (recent) progress towards it.   2018 KAIST Math. Colloquium Spatially balanced sampling Yves Tillé  (Institute of Statistics, University of Neuchatel) 2018-10-04   Spatial sampling is particularly important for environmental statistics. A simple reasoning developed in Grafström and Tillé (2013) shows that under a self-correlated linear model, it is more efficient to select a well-spread sample in space. If we select two neighbouring units in a sample, we will tend to collect partially redundant information. Grafström and Lundström (2013) discuss at length the concept of spreading, also known as spatial balancing and its implication on estimation. The Generalized Random Tesselation Sampling GRTS design has been proposed by Stevens Jr. and Olsen (1999, 2004, 2003) to select spread samples. The pivotal method has been proposed by Deville and Tillé (2000). Grafström et al. (2012) proposed to use the pivotal method for spatial sampling. This method, called the local pivotal method, consists, at each step, in comparing two neighboring units. If the probability of one of these two units is increased, the probability of the other is decreased, which induces a repulsion between the units. The natural extension of this idea is to confront a group of units. The local pivot method was generalized by Grafström and Tillé (2013) to provide samples that are both well-balanced in space and balanced on the totals of the auxiliary variables. This method is called the local cube method. We also propose a new method that enables us to select spreader samples that all existing methods and allows the construction of periodic sampling plans when these plans exist.   2018 Discrete Math 세미나 Mekler’s Construction on NTP1 Theory 안진후 (연세대학교) 2018-10-01   Any structure whose language is finite has a model of graph theory which is bi-interpretable with it. From this idea, Mekler further developed a way of interpreting a model into a group. This Mekler’s construction preserves various model-theoretic properties such as stability, simplicity, and NTP2, thus helps us find new group examples in model theory. In this talk, I will introduce to you what Mekler’s construction is and briefly show that this preserves NTP1.   2018 KAIST Math. Colloquium Optimal cluster recovery in the labeled stochastic block model 윤세영 (KAIST) 2018-09-27   We consider the problem of community detection or clustering in the labeled Stochastic Block Model (LSBM) with a finite number K of clusters of sizes linearly growing with the global population of items n. Every pair of items is labeled independently at random, and label ℓ appears with probability p(i,j,ℓ) between two items in clusters indexed by i and j, respectively. The objective is to reconstruct the clusters from the observation of these random labels. Clustering under the SBM and their extensions has attracted much attention recently. Most existing work aimed at characterizing the set of parameters such that it is possible to infer clusters either positively correlated with the true clusters, or with a vanishing proportion of misclassified items, or exactly matching the true clusters. We find the set of parameters such that there exists a clustering algorithm with at most smisclassified items in average under the general LSBM and for any s=o(n), which solves one open problem raised in Abbe et al 2015. We further develop an algorithm, based on simple spectral methods, that achieves this fundamental performance limit within O(n polylog(n)) computations and without the a-priori knowledge of the model parameters.   2018 Discrete Math 세미나 The extremal number of subdivisions Lee Joonkyung (Universität Hamburg) 2018-09-17   One of the cornerstones of extremal graph theory is a result of Füredi, later reproved and given due prominence by Alon, Krivelevich and Sudakov, saying that if H is a bipartite graph with maximum degree r on one side, then there is a constant C such that every graph with n vertices and C n2 – 1/r edges contains a copy of H. This result is tight up to the constant when H contains a copy of Kr,s with s sufficiently large in terms of r. We conjecture that this is essentially the only situation in which Füredi’s result can be tight and prove this conjecture for r = 2. More precisely, we show that if H is a C4-free bipartite graph with maximum degree 2 on one side, then there are positive constants C and δ such that every graph with n vertices and C n3/2 – δ edges contains a copy of H. This answers a question by Erdős from 1988. The proof relies on a novel variant of the dependent random choice technique which may be of independent interest. This is joint work with David Conlon.   2018 Discrete Math 세미나 On the off-diagonal Erdős-Szekeres convex polygon problem 백진언 (NIMS) 2018-09-10   The infamous Erdős-Szekeres conjecture, posed in 1935, states that the minimum number ES(n) of points on a plane in general position (that is, no three colinear points) that guarantees a subset of n points in convex position is equal to 2(n-2) + 1. Despite many years of effort, the upper bound of ES(n) had not been better than O(4n – o(n)) until Suk proved the groundbreaking result ES(n)≤2n+o(n) in 2016. In this talk, we focus on a variant of this problem by Erdős, Tuza and Valtr regarding the number ETV(a, b, n) of points needed to force either an a-cup, b-cap or a convex n-gon for varying a, b and n. They showed ETV(a, b, n) > sum_{i=n-b}^{a-2} binom{n}{i-2} by supplying a set of points with no a-cup, b-cap nor a n-gon of that many number, and conjectured that the inequality cannot be improved. Due to their construction, the conjecture is in fact equivalent to the Erdős-Szekeres conjecture. However, even the simplest equality ETV(4, n, n) = binom{n+1}{2} + 1, which must be true if the Erdős-Szekeres conjecture is, has not been verified yet. To the best of our knowledge, the bound ETV(4, n, n) ≤ binom{n + 2}{2} – 1, mentioned by Balko and Valtr in 2015, is currently the best bound known in literature. The talk is divided into two parts. First, we introduce the mentioned works on the Erdős-Szekeres conjecture and observe that the argument of Suk can be directly adapted to prove an improved bound of ETV(a, n, n). Then we show the bound ETV(4, n, n) ≤ binom{n+2}{2} – C sqrt{n} for a fixed constant C>0, improving the previously known best bound of Balko and Valtr.   최석정 강의실 기념 강연회 라틴방진의 응용과 최석정 9차 직교라틴방진의 특성 송홍엽 (연세대학교) 2018-09-07     최석정 강의실 기념 강연회 조선 후기 수학의 발전과 그 특징 김영욱 (고려대학교) 2018-09-07     2018 KAIST 세미나 Enumerating sets of integers with multiplicative constraints Hong Liu (University of Warwick, Warwick, UK) 2018-09-03   Counting problems on sets of integers with additive constraints have been extensively studied. In contrast, the counting problems for sets with multiplicative constraints remain largely unexplored. In this talk, we will discuss two such recent results, one on primitive sets and the other on multiplicative Sidon sets. Based on joint work with Peter Pach, and with Peter Pach and Richard Palincza.   2018 KAIST 세미나 Kazhdan type theorem for manifolds and complexes Chenxi Wu (Rutgers University) 2018-08-14   This is a collaboration with Harry Baik and Farbod Shokrieh. We generalized a classical theorem by Kazhdan on the convergence of canonical metric under a sequence of regular covers to the case of metrizable complexes as well as Riemannian manifolds.   2018 Discrete Math 세미나 The Art Gallery Problem is ∃R-complete Tillmann Miltzow (Université Libre de Bruxelles, Brussels) 2018-07-24   We prove that the art gallery problem is equivalent under polynomial time reductions to deciding whether a system of polynomial equations over the real numbers has a solution. The art gallery problem is a classical problem in computational geometry. Given a simple polygon P and an integer k, the goal is to decide if there exists a set G of k guards within P such that every point p∈P is seen by at least one guard g∈G. Each guard corresponds to a point in the polygon P, and we say that a guard g sees a point p if the line segment pg is contained in P. The art gallery problem has stimulated extensive research in geometry and in algorithms. However, the complexity status of the art gallery problem has not been resolved. It has long been known that the problem is NP-hard, but no one has been able to show that it lies in NP. Recently, the computational geometry community became more aware of the complexity class ∃R. The class ∃R consists of problems that can be reduced in polynomial time to the problem of deciding whether a system of polynomial equations with integer coefficients and any number of real variables has a solution. It can be easily seen that NP⊆∃R. We prove that the art gallery problem is ∃R-complete, implying that (1) any system of polynomial equations over the real numbers can be encoded as an instance of the art gallery problem, and (2) the art gallery problem is not in the complexity class NP unless NP=∃R. As a corollary of our construction, we prove that for any real algebraic number α there is an instance of the art gallery problem where one of the coordinates of the guards equals α in any guard set of minimum cardinality. That rules out many geometric approaches to the problem. This is joint work with Mikkel Abrahamsen and Anna Adamaszek.   Intensive Lecture Series by Ron Aharoni Lectures on topological methods in combinatorics -7 Ron Aharoni (Technion, Israel) 2018-07-19   The lectures will give an introduction to the application of topological methods in matching theory, graph theory, and combinatorics. Topics that will be covered: – A topological extension of Hall’s theorem – combinatorial applications of the nerve theorem – d-Leray complexes and rainbow matchings – Matroid complexes and applications – Open problems   Intensive Lecture Series by Ron Aharoni Lectures on topological methods in combinatorics -8 Ron Aharoni (Technion, Israel) 2018-07-19   The lectures will give an introduction to the application of topological methods in matching theory, graph theory, and combinatorics. Topics that will be covered: – A topological extension of Hall’s theorem – combinatorial applications of the nerve theorem – d-Leray complexes and rainbow matchings – Matroid complexes and applications – Open problems   Intensive Lecture Series by Ron Aharoni Lectures on topological methods in combinatorics -9 Ron Aharoni (Technion, Israel) 2018-07-19   The lectures will give an introduction to the application of topological methods in matching theory, graph theory, and combinatorics. Topics that will be covered: – A topological extension of Hall’s theorem – combinatorial applications of the nerve theorem – d-Leray complexes and rainbow matchings – Matroid complexes and applications – Open problems   Intensive Lecture Series by Ron Aharoni Lectures on topological methods in combinatorics -4 Ron Aharoni (Technion, Israel) 2018-07-18   The lectures will give an introduction to the application of topological methods in matching theory, graph theory, and combinatorics. Topics that will be covered: – A topological extension of Hall’s theorem – combinatorial applications of the nerve theorem – d-Leray complexes and rainbow matchings – Matroid complexes and applications – Open problems   Intensive Lecture Series by Ron Aharoni Lectures on topological methods in combinatorics -5 Ron Aharoni (Technion, Israel) 2018-07-18   The lectures will give an introduction to the application of topological methods in matching theory, graph theory, and combinatorics. Topics that will be covered: – A topological extension of Hall’s theorem – combinatorial applications of the nerve theorem – d-Leray complexes and rainbow matchings – Matroid complexes and applications – Open problems   Intensive Lecture Series by Ron Aharoni Lectures on topological methods in combinatorics -6 Ron Aharoni (Technion, Israel) 2018-07-18   The lectures will give an introduction to the application of topological methods in matching theory, graph theory, and combinatorics. Topics that will be covered: – A topological extension of Hall’s theorem – combinatorial applications of the nerve theorem – d-Leray complexes and rainbow matchings – Matroid complexes and applications – Open problems   Intensive Lecture Series by Ron Aharoni Lectures on topological methods in combinatorics -1  Ron Aharoni (Technion, Israel) 2018-07-17   The lectures will give an introduction to the application of topological methods in matching theory, graph theory, and combinatorics. Topics that will be covered: – A topological extension of Hall’s theorem – combinatorial applications of the nerve theorem – d-Leray complexes and rainbow matchings – Matroid complexes and applications – Open problems   Intensive Lecture Series by Ron Aharoni Lectures on topological methods in combinatorics -2 Ron Aharoni (Technion, Israel) 2018-07-17   The lectures will give an introduction to the application of topological methods in matching theory, graph theory, and combinatorics. Topics that will be covered: – A topological extension of Hall’s theorem – combinatorial applications of the nerve theorem – d-Leray complexes and rainbow matchings – Matroid complexes and applications – Open problems   Intensive Lecture Series by Ron Aharoni Lectures on topological methods in combinatorics -3 Ron Aharoni (Technion, Israel) 2018-07-17   The lectures will give an introduction to the application of topological methods in matching theory, graph theory, and combinatorics. Topics that will be covered: – A topological extension of Hall’s theorem – combinatorial applications of the nerve theorem – d-Leray complexes and rainbow matchings – Matroid complexes and applications – Open problems   Intensive Lectures on Moduli of differentials by Dawei Chen Moduli of differentials -5 Dawei Chen (Boston College) 2018-07-12   An Abelian differential defines a flat metric such that the underlying Riemann surface can be realized as a polygon whose edges are pairwise identified via translation. Varying the shape of such polygons induces a GL(2,R)-action on the moduli space of Abelian differentials, called Teichmueller dynamics, whose study has provided fascinating results and opened new avenues to many fields in mathematics. In the first lecture I will give an accessible introduction to this subject, with a focus on its connections to billiard dynamics, enumerative geometry, and arithmetic geometry. In the remaining lectures I will explain how to use techniques in algebraic geometry to study various problems in Teichmueller dynamics, including compactification, birational geometry, cycle class computation, etc. A number of recent developments and open problems will be mentioned.   Intensive Lectures on Moduli of differentials by Dawei Chen Moduli of differentials -3 Dawei Chen (Boston College) 2018-07-11   An Abelian differential defines a flat metric such that the underlying Riemann surface can be realized as a polygon whose edges are pairwise identified via translation. Varying the shape of such polygons induces a GL(2,R)-action on the moduli space of Abelian differentials, called Teichmueller dynamics, whose study has provided fascinating results and opened new avenues to many fields in mathematics. In the first lecture I will give an accessible introduction to this subject, with a focus on its connections to billiard dynamics, enumerative geometry, and arithmetic geometry. In the remaining lectures I will explain how to use techniques in algebraic geometry to study various problems in Teichmueller dynamics, including compactification, birational geometry, cycle class computation, etc. A number of recent developments and open problems will be mentioned.   Intensive Lectures on Moduli of differentials by Dawei Chen Moduli of differentials -4 Dawei Chen (Boston College) 2018-07-11   An Abelian differential defines a flat metric such that the underlying Riemann surface can be realized as a polygon whose edges are pairwise identified via translation. Varying the shape of such polygons induces a GL(2,R)-action on the moduli space of Abelian differentials, called Teichmueller dynamics, whose study has provided fascinating results and opened new avenues to many fields in mathematics. In the first lecture I will give an accessible introduction to this subject, with a focus on its connections to billiard dynamics, enumerative geometry, and arithmetic geometry. In the remaining lectures I will explain how to use techniques in algebraic geometry to study various problems in Teichmueller dynamics, including compactification, birational geometry, cycle class computation, etc. A number of recent developments and open problems will be mentioned.   Intensive Lectures on Moduli of differentials by Dawei Chen Moduli of differentials -1 Dawei Chen (Boston College) 2018-07-10   An Abelian differential defines a flat metric such that the underlying Riemann surface can be realized as a polygon whose edges are pairwise identified via translation. Varying the shape of such polygons induces a GL(2,R)-action on the moduli space of Abelian differentials, called Teichmueller dynamics, whose study has provided fascinating results and opened new avenues to many fields in mathematics. In the first lecture I will give an accessible introduction to this subject, with a focus on its connections to billiard dynamics, enumerative geometry, and arithmetic geometry. In the remaining lectures I will explain how to use techniques in algebraic geometry to study various problems in Teichmueller dynamics, including compactification, birational geometry, cycle class computation, etc. A number of recent developments and open problems will be mentioned.   Intensive Lectures on Moduli of differentials by Dawei Chen Moduli of differentials -2 Dawei Chen (Boston College) 2018-07-10   An Abelian differential defines a flat metric such that the underlying Riemann surface can be realized as a polygon whose edges are pairwise identified via translation. Varying the shape of such polygons induces a GL(2,R)-action on the moduli space of Abelian differentials, called Teichmueller dynamics, whose study has provided fascinating results and opened new avenues to many fields in mathematics. In the first lecture I will give an accessible introduction to this subject, with a focus on its connections to billiard dynamics, enumerative geometry, and arithmetic geometry. In the remaining lectures I will explain how to use techniques in algebraic geometry to study various problems in Teichmueller dynamics, including compactification, birational geometry, cycle class computation, etc. A number of recent developments and open problems will be mentioned.   Intensive Lecture Series by Jaehoon Kim Lecture 10 : The absorbing method II Jaehoon Kim (Birmingham University, UK) 2018-06-29    In this lecture, we aim to learn several techniques to find sufficient conditions on a dense graph G to contain a sparse graph H as a subgraph.   Intensive Lecture Series by Jaehoon Kim Lecture 9 : The absorbing method I Jaehoon Kim (Birmingham University, UK) 2018-06-29    In this lecture, we aim to learn several techniques to find sufficient conditions on a dense graph G to contain a sparse graph H as a subgraph.

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