Gary Gordon and Liz McMahon: Generalizations of Crapo's Beta Invariant
Abstract: Crapo's beta invariant was defined by Henry Crapo in the 1960s. For a matroid M, the invariant β(M) is the non-negative integer that is the coefficient of the x term of the Tutte polynomial. Crapo proved that β(M) is greater than 0 if and only if M is connected and M is not a loo
From playlist Combinatorics
Joseph Bonin: Delta-matroids as subsystems of sequences of Higgs lifts
Abstract: Delta-matroids generalize matroids. In a delta-matroid, the counterparts of bases, which are called feasible sets, can have different sizes, but they satisfy a similar exchange property in which symmetric differences replace set differences. One way to get a delta-matroid is to t
From playlist Combinatorics
Yusuke Kobayashi: A weighted linear matroid parity algorithm
The lecture was held within the framework of the follow-up workshop to the Hausdorff Trimester Program: Combinatorial Optimization. Abstract: The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so gener
From playlist Follow-Up-Workshop "Combinatorial Optimization"
Singular Hodge theory of matroids - Jacob Matherne
Short talks by postdoctoral members Topic: Singular Hodge theory of matroids Speaker: Jacob Matherne Affiliation: Member, School of Mathematics Date: Oct 1, 2018 For more video please visit http://video.ias.edu
From playlist Mathematics
Anna De Mier: Approximating clutters with matroids
Abstract: There are several clutters (antichains of sets) that can be associated with a matroid, as the clutter of circuits, the clutter of bases or the clutter of hyperplanes. We study the following question: given an arbitrary clutter Λ, which are the matroidal clutters that are closest
From playlist Combinatorics
Yuval Filmus: Monotone Submodular Optimization over a Matroid
We consider the NP-hard problem of maximizing a monotone submodular function over a matroid constraint. Vondrak's continuous greedy algorithm achieves the best possible approximation ratio 1-1/e using continuous methods. Can the same be accomplished combinatorially? We show that this is ar
From playlist HIM Lectures 2015
Nonlinear algebra, Lecture 13: "Polytopes and Matroids ", by Mateusz Michalek
This is the thirteenth lecture in the IMPRS Ringvorlesung, the advanced graduate course at the Max Planck Institute for Mathematics in the Sciences.
From playlist IMPRS Ringvorlesung - Introduction to Nonlinear Algebra
Strongly log concave polynomials...Bases of Matroids - Shayan Oveis Gharan
More videos on http://video.ias.edu
From playlist Mathematics
Victor Chepoi: Simple connectivity, local to global, and matroids
Victor Chepoi: Simple connectivity, local-to-global, and matroids A basis graph of a matroid M is the graph G(M) having the bases of M as the vertex-set and the pairs of bases differing by an elementary exchange as edges. Basis graphs of matroids have been characterized by S.B. Maurer, J.
From playlist HIM Lectures 2015
Gyula Pap: Linear matroid matching in the oracle model
Gyula Pap: Linear matroid matching in the oracle model Linear matroid matching is understood as a special case of matroid matching when the matroid is given with a matrix representation. However, for certain examples of linear matroids, the matrix representation is not given, and actuall
From playlist HIM Lectures 2015
Zoltán Szigeti: Packing of arborescences with matroid constraints via matroid intersection
The lecture was held within the framework of the follow-up workshop to the Hausdorff Trimester Program: Combinatorial Optimization. Abstract: Edmonds characterized digraphs having a packing of k spanning arborescences in terms of connectivity and later in terms of matroid intersection. D
From playlist Follow-Up-Workshop "Combinatorial Optimization"
Sahil Singla: Online Matroid Intersection Beating Half for Random Arrival
We study a variant of the online bipartite matching problem that we call the online matroid intersection problem. For two matroids M1 and M2 defined on the same ground set E, the problem is to design an algorithm that constructs the largest common independent set in an online fashion. At e
From playlist HIM Lectures 2015
Max Wakefield, Research talk - 9 February 2015
Max Wakefield (United States Naval Academy) - Research talk http://www.crm.sns.it/course/4049/ We study a few different perspectives (combinatorics, geometry, and algebra) of a new polynomial attached to a matroid. First we define the polynomial combinatorially and compute it for certain
From playlist Algebraic topology, geometric and combinatorial group theory - 2015
The log-concavity conjecture and the tropical Laplacian - June Huh
June Huh Princeton University; Veblen Fellow, School of Mathematics February 17, 2015 The log-concavity conjecture predicts that the coefficients of the chromatic (characteristic) polynomial of a matroid form a log-concave sequence. The known proof for realizable matroids uses algebraic g
From playlist Mathematics
Quantum Geometry of Matroids by Dhruv Ranganathan
PROGRAM COMBINATORIAL ALGEBRAIC GEOMETRY: TROPICAL AND REAL (HYBRID) ORGANIZERS: Arvind Ayyer (IISc, India), Madhusudan Manjunath (IITB, India) and Pranav Pandit (ICTS-TIFR, India) DATE & TIME: 27 June 2022 to 08 July 2022 VENUE: Madhava Lecture Hall and Online Algebraic geometry is t
From playlist Combinatorial Algebraic Geometry: Tropical and Real (HYBRID)