Doowon Koh (고두원), On the cone restriction conjecture in four dimensions and applications in incidence geometry
2021-02-09 16:30 - 17:30 (Asia/Seoul) | Room B232, IBS (기초과학연구원)
Main purpose of this talk is to introduce a connection between restriction estimates for cones and point-sphere incidence theorems in the finite field setting. First, we review the finite field restriction problem for cones and address new results on the conical restriction problems. In particular, we establish the restriction conjecture for the cone in four dimensions. Second, we study how to apply the conical restriction results to the point-sphere incidence bounds. As a consequence, we obtain sharp point-sphere incidence bounds when sphere sets are not too big.

Jie Ma (马杰), Non-repeated cycle lengths and Sidon sequences
2021-02-10 16:30 - 17:30 | Zoom ID: 869 4632 6610 (ibsdimag)
We prove a conjecture of Boros, Caro, Furedi and Yuster on the maximum number of edges in a 2-connected graph without repeated cycle lengths, which is a restricted version of a longstanding problem of Erdos. Our proof together with the matched lower bound construction of Boros, Caro, Furedi and Yuster show that this problem can be conceptually reduced to the seminal problem of finding the maximum Sidon sequences in number theory. Joint work with Tianchi Yang.

Martin Ziegler, Quantitative Coding and Complexity Theory of Continuous Data
2021-02-16 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
Specifying a computational problem requires fixing encodings for input and output: encoding graphs as adjacency matrices, characters as integers, integers as bit strings, and vice versa. For such discrete data, the actual encoding is usually straightforward and/or complexity-theoretically inessential (up to polynomial time, say).
But concerning continuous data, already real numbers naturally suggest various encodings with very different computational properties.
We recall the existing qualitative theory of computably ‘sensible’ encodings of topological spaces; and we newly develop the quantitative theory of complexity-theoretically ‘sensible’ encodings of metric spaces.
Joint work with Donghyun Lim.

David Wood, Tree densities of sparse graph classes
2021-02-17 10:00 - 11:00 | Zoom ID: 869 4632 6610 (ibsdimag)
This talk considers the following question at the intersection of extremal and structural graph theory: What is the maximum number of copies of a fixed forest $T$ in an $n$-vertex graph in a graph class $mathcal{G}$ as $nto infty$? I will answer this question for a variety of sparse graph classes $mathcal{G}$. In particular, we show that the answer is $Theta(n^{alpha_d(T)})$ where $alpha_d(T)$ is the size of the largest stable set in the subforest of $T$ induced by the vertices of degree at most $d$, for some integer $d$ that depends on $mathcal{G}$. For example, when $mathcal{G}$ is the class of $k$-degenerate graphs then $d=k$; when $mathcal{G}$ is the class of graphs containing no $K_{s,t}$-minor ($tgeq s$) then $d=s-1$; and when $mathcal{G}$ is the class of $k$-planar graphs then $d=2$. All these results are in fact consequences of a single lemma in terms of a finite set of excluded subgraphs. This is joint work with Tony Huynh (arXiv:2009.12989).

Minki Kim (김민기), Rainbow paths and rainbow matchings
2021-02-23 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
We prove that if $n geq 3$, then any family of $3n-3$ sets of matchings of size $n$ in any graph has a rainbow matching of size $n$. This improves on a previous result, in which $3n-3$ is replaced by $3n-2$. We also prove a “cooperative” generalization: for $t > 0$ and $n geq 3$, any $3n-4+t$ sets of edges, the union of every $t$ of which contains a matching of size $n$, have rainbow matching of size $n$. This is joint work with Ron Aharoni, Joseph Briggs, and Jinha Kim.

Kevin Hendrey, A unified half-integral Erdős-Pósa theorem for cycles in graphs labelled by multiple abelian groups
2021-03-02 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
Erdős and Pósa proved in 1965 that there is a duality between the maximum size of a packing of cycles and the minimum size of a vertex set hitting all cycles. Such a duality does not hold if we restrict to odd cycles. However, in 1999, Reed proved an analogue for odd cycles by relaxing packing to half-integral packing. We prove a far-reaching generalisation of the theorem of Reed; if the edges of a graph are labelled by finitely many abelian groups, then there is a duality between the maximum size of a half-integral packing of cycles whose values avoid a fixed finite set for each abelian group and the minimum size of a vertex set hitting all such cycles.
A multitude of natural properties of cycles can be encoded in this setting, for example cycles of length at least $ell$, cycles of length $p$ modulo $q$, cycles intersecting a prescribed set of vertices at least $t$ times, and cycles contained in given $mathbb{Z}_2$-homology classes in a graph embedded on a fixed surface. Our main result allows us to prove a duality theorem for cycles satisfying a fixed set of finitely many such properties.
This is joint work with J. Pascal Gollin, Ken-ichi Kawarabayashi, O-joung Kwon, and Sang-il Oum.

Debsoumya Chakraborti, Some classical problems in graph saturation
2021-03-09 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
Graph saturation is one of the oldest areas of investigation in extremal combinatorics. A graph $G$ is called $F$-saturated if $G$ does not contain a subgraph isomorphic to $F$, but the addition of any edge creates a copy of $F$. The function $operatorname{sat}(n,F)$ is defined to be the minimum number of edges in an $n$-vertex $F$-saturated graph.
In the first half of the talk, we will discuss a generalization of Erdős-Hajnal-Moon theorem (1964), which determined the value of $operatorname{sat}(n,K_s)$. We resolve one of the fundamental questions of minimizing the number of cliques of size $r$ in a $K_s$-saturated graph for all sufficiently large number of vertices, confirming a conjecture of Kritschgau, Methuku, Tait, and Timmons. We further establish a corresponding stability result.
In the second half, we will focus on a central conjecture in graph saturation made by Tuza (1986), which states that for every graph $F$, the limit $lim_{n rightarrow infty} frac{operatorname{sat}(n,F)}{n}$ exists. We make progress in the negative direction of this conjecture.
This talk will be based on a joint work with Po-Shen Loh.

Se-Young Yun (윤세영), Regret in Online Recommendation Systems
2021-03-16 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
We propose a theoretical analysis of recommendation systems in an online setting, where items are sequentially recommended to users over time. In each round, a user, randomly picked from a population of m users, requests a recommendation. The decision-maker observes the user and selects an item from a catalogue of n items. Importantly, an item cannot be recommended twice to the same user. The probabilities that a user likes each item are unknown. The performance of the recommendation algorithm is captured through its regret, considering as a reference an Oracle algorithm aware of these probabilities. We investigate various structural assumptions on these probabilities: we derive for each structure regret lower bounds, and devise algorithms achieving these limits. Interestingly, our analysis reveals the relative weights of the different components of regret: the component due to the constraint of not presenting the same item twice to the same user, that due to learning the chances users like items, and finally that arising when learning the underlying structure.
This is joint work with Kaito Ariu, Narae Ryu, and Alexandre Proutière.

Yixin Cao (操宜新), Recognizing (unit) interval graphs by zigzag graph searches
2021-03-17 17:00 - 18:00 | Room B232, IBS (기초과학연구원)
Corneil, Olariu, and Stewart [SODA 1998; SIAM Journal on Discrete Mathematics 2009] presented a recognition algorithm for interval graphs by six graph searches. Li and Wu [Discrete Mathematics & Theoretical Computer Science 2014] simplified it to only four. The great simplicity of the latter algorithm is however eclipsed by the complicated and long proofs. The main purpose of this paper is to present a new and significantly shorter proof for Li and Wu’s algorithm, as well as a simpler implementation. We also give a self-contained presentation of the recognition algorithm of Corneil [Discrete Applied Mathematics 2004] for unit interval graphs, based on three sweeps of graph searches. Moreover, we show that two sweeps are already sufficient. Toward the proofs of the main results, we make several new structural observations that might be of independent interests.

Hong Liu (刘鸿), Nested cycles with no geometric crossing
2021-03-22 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
In 1975, Erdős asked the following question: what is the smallest function $f(n)$ for which all graphs with $n$ vertices and $f(n)$ edges contain two edge-disjoint cycles $C_1$ and $C_2$, such that the vertex set of $C_2$ is a subset of the vertex set of $C_1$ and their cyclic orderings of the vertices respect each other? We prove the optimal linear bound $f(n)=O(n)$ using sublinear expanders.
This is joint work with Irene Gil Fernández, Jaehoon Kim and Younjin Kim.

Édouard Bonnet, Twin-width and ordered binary structures
2021-03-24 17:00 - 18:00 | Zoom ID: 869 4632 6610 (ibsdimag)
The twin-width of a graph G can be defined as the least integer d such that there is a sequence of length |V(G)| of (strictly) coarser and coarser partitions of its vertex set V(G), and every part X of every partition P of the sequence has at most d other parts Y of P with both at least one edge and at least one non-edge between X and Y. Twin-width is closely tied to total orders on the vertices, and can be extended to general binary structures. We will thus consider the twin-width of ordered binary structures, or if you prefer, matrices on a finite alphabet. This turns out to be key in understanding combinatorial, algorithmic, and model-theoretic properties of (hereditary) classes of those objects. We will see several characterizations of bounded twin-width for these classes. The main consequences in the three domains read as follows.

Enumerative combinatorics: All the classes of 0,1-matrices with superexponential growth have growth at least n! (in turn resolving a conjecture of Balogh, Bollobás, and Morris on the growth of hereditary classes of ordered graphs).
Algorithms: First-order model checking of ordered binary structures is tractable exactly when the twin-width is bounded.
Finite model theory: Monadically-dependent and dependent hereditary classes of ordered binary structures are the same.

In addition we get a fixed-parameter algorithm approximating matrix twin-width within a function of the optimum, which is still missing for unordered graphs.
Joint work with Ugo Giocanti, Patrice Ossona de Mendez, and Stéphan Thomassé. Similar results have been obtained independently by Pierre Simon and Szymon Toruńczyk.

Casey Tompkins, 3-uniform hypergraphs avoiding a cycle of length four
2021-03-30 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
We show that that the maximum number of of edges in a $3$-uniform hypergraph without a Berge-cycle of length four is at most $(1+o(1)) frac{n^{3/2}}{sqrt{10}}$. This improves earlier estimates by Győri and Lemons and by Füredi and Özkahya. Joint work with Ergemlidze, Győri, Methuku, Salia.

Sophie Spirkl, Pure pairs in ordered graphs
2021-04-01 10:00 - 11:00 | Zoom ID: 869 4632 6610 (ibsdimag)
A pure pair in a graph G is a pair of subsets A, B of the vertex set of G such that in G, either all of the edges or none of the edges between A and B are present. Pure pairs have been studied recently motivated by their connections to the Erdos-Hajnal conjecture.
In this talk, I will discuss the topic of pure pairs in ordered graphs, that is, graphs with a linear ordering on their vertex set. If we exclude a graph H as an ordered induced subgraph, how large a pure pair can we guarantee? I will talk about how the answer differs from the case of unordered graphs and show some of the techniques used.
Based on joint work with Maria Chudnovsky, Jacob Fox, Alex Scott, and Paul Seymour.

Rutger Campbell, Matroid orientability and representability
2021-04-06 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
In this talk we will have a brief introduction to oriented matroids and their relation to real-representability.

Michał Pilipczuk, Structural properties of powers of sparse graphs
2021-04-07 17:00 - 18:00 | Zoom ID: 869 4632 6610 (ibsdimag)
For a graph G and an integer d, the dth power of G is the graph $G^d$ on the same vertex set as G where two vertices are considered adjacent if and only if they are at distance at most d in G. Assuming that G is sparse, what can we say about the structure in $G^d$? Certainly $G^d$ can be dense, as the square of a star is a complete graph, but $G^d$ still retains many properties that can be derived from the sparsity of G. We will present some recent results in this spirit, in particular connected to colorings and to the Erdős-Hajnal property, assuming that G is drawn from a fixed class of bounded expansion or from a fixed nowhere dense class. The talk will be based on the recent papers: “Clustering Powers of Sparse Graphs” (with J. Nešetřil, P. Ossona de Mendez, and X. Zhu) and “Erdős-Hajnal properties for powers of sparse graphs” (with M. Briański, P. Micek, and M. Seweryn).

William Overman, Some Ordered Ramsey Numbers of Graphs on Four Vertices
2021-04-13 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
Ordered Ramsey numbers were introduced in 2014 by Conlon, Fox, Lee, and Sudakov. Their results included upper bounds for general graphs and lower bounds showing separation from classical Ramsey numbers. We show the first nontrivial results for ordered Ramsey numbers of specific small graphs. In particular we prove upper bounds for orderings of graphs on four vertices, and determine some numbers exactly using SAT solvers for lower bounds. These results are in the spirit of exact calculations for classical Ramsey numbers and use only elementary combinatorial arguments.
This is joint work with Jeremy Alm, Kayla Coffey, and Carolyn Langhoff.

István Tomon, Ramsey properties of semilinear graphs
2021-04-14 17:00 - 18:00 | Zoom ID: 869 4632 6610 (ibsdimag)
A graph $G$ is semilinear of bounded complexity if the vertices of $G$ are elements of $mathbb{R}^{d}$, and the edges of $G$ are defined by the sign patterns of $t$ linear functions, where $d$ and $t$ are constants. In this talk, I will present several results about the symmetric and asymmetric Ramsey properties of semilinear graphs. Some interesting instances of such graphs are intersection graphs of boxes, interval overlap graphs, and shift graphs, so our results extend several well known theorems about the Ramsey and coloring properties of these geometrically defined graphs.

Sang-il Oum (엄상일), What is an isotropic system?
2021-04-20 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
Bouchet introduced isotropic systems in 1983 unifying some combinatorial features of binary matroids and 4-regular graphs. The concept of isotropic system is a useful tool to study vertex-minors of graphs and yet it is not well known. I will give an introduction to isotropic systems.

Reinhard Diestel, Tangles of set separations: a novel clustering method and type recognition in machine learning
2021-04-21 17:00 - 18:00 | Zoom ID: 869 4632 6610 (ibsdimag)
Traditional clustering identifies groups of objects that share certain qualities. Tangles do the converse: they identify groups of qualities that typically occur together. They can thereby discover, relate, and structure types: of behaviour, political views, texts, or proteins. Tangles offer a new, quantitative, paradigm for grouping phenomena rather than things. They can identify key phenomena that allow predictions of others. Tangles also offer a new paradigm for clustering in large data sets.
The mathematical theory of tangles has its origins in the theory of graph minors developed by Robertson and Seymour. It has recently been axiomatized in a way that makes it applicable to a wide range of contexts outside mathematics: from clustering in data science to predicting customer behaviour in economics, from DNA sequencing and drug development to text analysis and machine learning.
This very informal talk will not show you the latest intricacies of abstract tangle theory (for which you can find links on the tangle pages of my website), but to win you over to join our drive to develop real tangle applications in areas as indicated above. We have some software to share, but are looking for people to try it out with us on real-world examples!
Here are some introductory pages from a book I am writing on this, which may serve as an extended abstract: https://arxiv.org/abs/2006.01830

Jungho Ahn (안정호), Well-partitioned chordal graphs with the obstruction set and applications
2021-04-27 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
We introduce a new subclass of chordal graphs that generalizes split graphs, which we call well-partitioned chordal graphs. Split graphs are graphs that admit a partition of the vertex set into cliques that can be arranged in a star structure, the leaves of which are of size one. Well-partitioned chordal graphs are a generalization of this concept in the following two ways. First, the cliques in the partition can be arranged in a tree structure, and second, each clique is of arbitrary size. We mainly provide a characterization of well-partitioned chordal graphs by forbidden induced subgraphs and give a polynomial-time algorithm that given any graph, either finds an obstruction or outputs a partition of its vertex set that asserts that the graph is well-partitioned chordal. We demonstrate the algorithmic use of this graph class by showing that two variants of the problem of finding pairwise disjoint paths between k given pairs of vertices are in FPT, parameterized by k, on well-partitioned chordal graphs, while on chordal graphs, these problems are only known to be in XP. From the other end, we introduce some problems that are polynomial-time solvable on split graphs but become NP-complete on well-partitioned chordal graphs.
This is joint work with Lars Jaffke, O-joung Kwon, and Paloma T. Lima.

Raul Lopes, Adapting the Directed Grid Theorem into an FPT Algorithm
2021-05-06 10:00 - 11:00 | Zoom ID: 869 4632 6610 (ibsdimag)
The Grid Theorem of Robertson and Seymour [JCTB, 1986] is one of the most important tools in the field of structural graph theory, finding numerous applications in the design of algorithms for undirected graphs. An analogous version of the Grid Theorem in digraphs was conjectured by Johnson et al. [JCTB, 2001] , and proved by Kawarabayashi and Kreutzer [STOC, 2015]. They showed that there is a function f(k) such that every digraph of directed tree-width at least f(k) contains a cylindrical grid of order k as a butterfly minor and stated that their proof can be turned into an XP algorithm, with parameter k, that either constructs a decomposition of the appropriate width, or finds the claimed large cylindrical grid as a butterfly minor.
In this talk, we present the ideas used in our adaptation of the Directed Grid Theorem into an FPT algorithm. We provide two FPT algorithms with parameter k. The first one either produces an arboreal decomposition of width 3k-2 or finds a haven of order k in a digraph D. The second one uses a bramble B that naturally occurs in digraphs of large directed tree-width to find a well-linked set of order k that is contained in the set of vertices of a path hitting all elements of B. As tools to prove these results, we show how to solve a generalized version of the problem of finding balanced separators for a given set of vertices T in FPT time with parameter |T|.
Joint work with Victor Campos, Ana Karolinna Maia, and Ignasi Sau.

Hong Liu, Sublinear expander and embeddings sparse graphs
2021-05-06 16:15 - 17:15 | Zoom
A notion of sublinear expander has played a central role in the resolutions of a couple of long-standing conjectures in embedding problems in graph theory, including e.g. the odd cycle problem of Erdős and Hajnal that the harmonic sum of odd cycle length in a graph diverges with its chromatic number. I will survey some of these developments.

Mark Siggers, The list switch homomorphism problem for signed graphs
2021-05-11 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
A signed graph is a graph in which each edge has a positive or negative sign. Calling two graphs switch equivalent if one can get from one to the other by the iteration of the local action of switching all signs on edges incident to a given vertex, we say that there is a switch homomorphism from a signed graph $G$ to a signed graph $H$ if there is a sign preserving homomorphism from $G’$ to $H$ for some graph $G’$ that is switch equivalent to $G$. By reductions to CSP this problem, and its list version, are known to be either polynomial time solvable or NP-complete, depending on $H$. Recently those signed graphs $H$ for which the switch homomorphism problem is in $P$ were characterised. Such a characterisation is yet unknown for the list version of the problem.
We talk about recent work towards such a characterisation and about how these problems fit in with bigger questions that still remain around the recent CSP dichotomy theorem.

Johannes Carmesin, A Whitney type theorem for surfaces: characterising graphs with locally planar embeddings
2021-05-12 17:00 - 18:00 | Zoom ID: 869 4632 6610 (ibsdimag)
Given a graph, how do we construct a surface so that the graph embeds in that surface in an optimal way? Thomassen showed that for minimum genus as optimality criterion, this problem would be NP-hard. Instead of minimum genus, here we use local planarity — and provide a polynomial algorithm.
Our embedding method is based on Whitney’s trick to use matroids to construct embeddings in the plane. Consequently we obtain a characterisation of the graphs admitting locally planar embeddings in surfaces in terms of a certain matroid being co-graphic.

Pascal Gollin, Enlarging vertex-flames in countable digraphs
2021-05-18 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
A rooted digraph is a vertex-flame if for every vertex v there is a set of internally disjoint directed paths from the root to v whose set of terminal edges covers all ingoing edges of v. It was shown by Lovász that every finite rooted digraph admits a spanning subdigraph which is a vertex-flame and large, where the latter means that it preserves the local connectivity to each vertex from the root. A structural generalisation of vertex-flames and largeness to infinite digraphs was given by Joó and the analogue of Lovász’ result for countable digraphs was shown.
In this talk, I present a strengthening of this result stating that in every countable rooted digraph each vertex-flame can be extended to a large vertex-flame.
Joint work with Joshua Erde and Attila Joó.

Benjamin Bumpus, Directed branch-width: A directed analogue of tree-width
2021-05-21 17:00 - 18:00 | Zoom ID: 869 4632 6610 (ibsdimag)
Many problems that are NP-hard in general become tractable on `structurally recursive’ graph classes. For example, consider classes of bounded tree- or clique-width. Since the 1990s, many directed analogues of tree-width have been proposed. However, many natural problems (e.g. directed HamiltonPath and MaxCut) remain intractable on such digraph classes of `bounded width’.
In this talk, I will introduce a new tree-width analogue for digraphs called directed branch-width which allows us to define digraph classes for which many problems (including directed HamiltonPath and MaxCut) become linear-time solvable. Furthermore, via the definition of directed branch-width, I will obtain a generalisation to digraphs of Gurski and Wanke’s characterization of graph classes of bounded tree-width in terms of their line graphs.
This is joint work with Kitty Meeks and William Pettersson.

Ben Lund, Limit shape of lattice Zonotopes
2021-05-25 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
A convex lattice polytope is the convex hull of a set of integral points. Vershik conjectured the existence of a limit shape for random convex lattice polygons, and three proofs of this conjecture were given in the 1990s by Bárány, by Vershik, and by Sinai. To state this old result more precisely, there is a convex curve $L subset [0,1]^2$ such that the following holds. Let $P$ be a convex lattice polygon chosen uniformly at random from the set of convex lattice polygons with vertices in $[0,N]^2$. Then, for $N$ sufficiently large, $(1/N)P$ will be arbitrarily close (in Hausdorff distance) to $L$ with high probability. It is an open question whether there exists a limit shape for three dimensional polyhedra.
I will discuss this problem and some relatives, as well as joint work with Bárány and Bureaux on the existence of a limit shape for lattice zonotopes in all dimensions.

Dimitrios M. Thilikos, Bounding Obstructions sets: the cases of apices of minor closed classes
2021-05-26 17:00 - 18:00 | Zoom ID: 869 4632 6610 (ibsdimag)
Given a minor-closed graph class ${cal G}$, the (minor) obstruction of ${cal G}$ is the set of all minor-minimal graphs not in ${cal G}$. Given a non-negative integer $k$, we define the $k$-apex of ${cal A}$ as the class containing every graph $G$ with a set $S$ of vertices whose removal from $G$ gives a graph on ${cal G}$. We prove that every obstruction of the $k$-apex of ${cal G}$ has size bounded by some 4-fold exponential function of $p(k)$ where p is a polynomial function whose degree depends on the size of the minor-obstructions of ${cal G}$. This bound drops to a 2-fold exponential one when ${cal G}$ excludes some apex graph as a minor (i.e., a graph in the $1$-apex of planar graphs).
Joint work with Ignasi Sau and Giannos Stamoulis.

Doowon Koh (고두원), Mattila-Sjölin type functions: A finite field model
2021-06-01 16:30 - 17:30 | Room B232, IBS (기초과학연구원)
Let $mathbb{F}_q$ be a finite field of order $q$ which is a prime power. In the finite field setting, we say that a function $phicolon mathbb{F}_q^dtimes mathbb{F}_q^dto mathbb{F}_q$ is a Mattila-Sjölin type function in $mathbb{F}_q^d$ if for any $Esubset mathbb{F}_q^d$ with $|E|gg q^{frac{d}{2}}$, we have $phi(E, E)=mathbb{F}_q$. The main purpose of this talk is to present the existence of such a function. More precisely, we will construct a concrete function $phi: mathbb{F}_q^4times mathbb{F}_q^4to mathbb{F}_q$ with $qequiv 3 mod{4}$ such that if $Esubset mathbb F_q^4$ with $|E|>q^2,$ then $phi(E,E)=mathbb F_q$. This is a joint work with Daewoong Cheong, Thang Pham, and Chun-Yen Shen.

Adam Zsolt Wagner, Constructions in combinatorics via neural networks
2021-06-02 17:00 - 18:00 | Zoom ID: 869 4632 6610 (ibsdimag)
Recently, significant progress has been made in the area of machine learning algorithms, and they have quickly become some of the most exciting tools in a scientist’s toolbox. In particular, recent advances in the field of reinforcement learning have led computers to reach superhuman level play in Atari games and Go, purely through self-play. In this talk, I will give a very basic introduction to neural networks and reinforcement learning algorithms. I will also indicate how these methods can be adapted to the “game” of trying to find a counterexample to a mathematical conjecture, and show some examples where this approach was successful.
