The students talks displayed in this page are ordered by alphabetical order of the speakers, with respect to their first names. See their schedule and venue on the linked pages.
We plan to record and upload videos of the talks when consent is granted by the speaker. Links to these will be made available on this page.
Our conference is going to feature talks from two invited speakers and 13 student speakers:
TBA
More information about Prof. Totzeck can be found here.
The combinatorial Grassmannian, also called the MacPhersonian, is a simplicial complex which is conjectured to approximate the real Grassmannian manifold in the sense that the two might be homotopy equivalent -- in other words, their global geometry must be very similar. If this was true, it would give rise to a method of combinatorializing vector bundles from which all characteristic class information could be recovered; this was shown in the 1993 paper of MacPherson where the combinatorial Grassmannian was first introduced as part of abstracting some methods used in a previous paper of his joint with Gelfand.
The MacPhersonian is built from the partially ordered set of all oriented matroids, and so alongside giving an introduction to the conjecture I also say a few words about them. The second half of the talk is dedicated to a new angle of attack of the conjecture that we developed, whereby we construct a diagram of spaces over the MacPhersonian, who when glued together give the Grassmannian, and where if all entries are contractible then the conjecture is proven to hold. In particular, this leads to a proof of three previously unknown cases of the conjecture. The talk is based on joint work with Pavle Blagojević.
Generating random spanning trees in a finite connected graph has gotten special attention since the nineties and several algorithms have been developed over the years. Special interest comes from Combinatorics and Computer Science. Nowadays, Uniform Spanning Trees are a fundamental source of conjectures in various research areas via several bijections.
In this talk, we present the fastest known method for generating a spanning tree uniformly at random that David Wilson introduced as a graduate student. In doing so, we provide some historical background and define the Stacks Picture.
This talk aims to be self-contained and is based on my master's thesis supervised by Gerónimo Uribe Bravo at the Instituto de Matemáticas, UNAM.
Stochastic Partial Differential Equations (SPDEs) are notoriously hard to make sense of rigorously, as the high irregularity of the noise make possible nonlinearities of the equation ill-defined. Whereas most of the progress in the last decade have been focused on the path-wise approaches based on the seminal work on rough-paths theory by Lyons, in this talk we will instead present a modern probabilistic martingale-based approaches. Such an approach is attractive, as such solutions arise naturally as macroscopic scaling limits of interacting particle systems. In particular, we will present recent results on the well-posedness of so-called fractional SPDEs which arise from long-range microscopic interactions that allow for jumps with infinite variance. This naturally extends similar results on scaling limits for interacting particle systems with jumps of finite variance.
Scheduling jobs onto parallel machines so as to minimize the makespan of any machine is one of the most prominent scheduling problems. The online variant of this problem, in which jobs are revealed one by one and have to be assigned to a machine irrevocably after their revelation, has been studied intensively as well. We consider a generalization of this problem, in which multiple subsets of jobs over the same ground set, called scenarios, have to be scheduled simultaneously. We undertake a competitive analysis of several online algorithms for this problem, in which the value of the output is compared to an offline optimum, i.e., an optimal solution under the knowledge of the entire instance. We also sketch some inapproximability results and connections to an online variant of the balanced hypergraph coloring problem.
A lattice is a finite subgroup of the space ℝd. The field of Geometry of Numbers is the intersection of Number Theory and Discrete and Convex Geometry that focuses on understanding various functionals on the family of lattice polytopes. Some of those functionals are the covering radius and lattice width, which were connected by a sequence of functionals called the covering minima by Kannan and Lovász in 1988. In this talk, we will introduce these functionals, put them into context of integer linear programming and give intuition for why we are motivated to study them further.
In this talk we present a model for growth in a multi-species population. We consider two genetic types competing for a limited amount of resources through a logistic branching process with mutation. We first study the frequency of the disadvantageous type and show that, once the population approaches the carrying capacity, such frequency converges to a diffusion process with drift. We then study the dynamics backward in time: we fix a time horizon at which the population is at carrying capacity and we study the ancestral relations of a sample of individuals . We prove that, provided that the advantageous and disadvantageous branching measures are ordered, this ancestral line process converges to the moment dual of the limiting diffusion. This talk is based on ongoing joint work with Julian Kern (WIAS).
Stochastic partial differential equations (SPDEs) and how to numerically solve them has been a growing area of mathematical research over the past three decades. In this talk, I will introduce SPDEs and some of the methods needed to solve them numerically. The concept of strong error estimates and convergence rates of a numerical scheme will be discussed. The example of a splitting scheme for the stochastic heat equation is used to illustrate the theory.
An understanding of Hilbert spaces and basic stochastic analysis is recommended.
The Skorokhod problem is a fundamental mathematical framework used to study diffusion processes with reflection boundary. This problem plays a crucial role in queueing theory and finance, where constraints arise naturally due to physical, financial, or operational limitations. While the classical problem addresses linear constraints, many practical systems necessitate extensions to nonlinear constraints.
In this talk, we begin with an overview of the classical Skorokhod problem and the extended Skorokhod problem, highlighting their key properties, solution methods, and applications. We examine the conditions under which solutions exist and are unique.
Building on this foundation, we introduce the extended Skorokhod problem with nonlinear boundary dynamics, motivated by applications in multi-dimensional stochastic systems and market interactions.
A pseudoline arrangement is a finite family of curves which behave like non-parallel lines, they are unbounded and cross pairwise. Surprisingly, these simple objects are in relation to a rich variety of other combinatorial structures, such as, for example, permutations, sorting networks, standard Young tableaux, certain kind of rhombic tilings and oriented matroids. Similarly to shuffling a deck of cards, we may generate random pseudoline arrangements using a Markov chain. We will see several such Markov chains. However, it is still an open problem to determine their mixing time, i.e. to answer the question how fast these Markov chains converge towards the uniform distribution.
Agent-based models (ABM) are used for studying complex systems by simulating interactions at the micro-level. This modelling approach allows us to understand socio-economic phenomena by examining the agents' behaviour and their collective impact within the system. However, ABMs are often plagued by the curse of dimensionality, making it challenging (if not impossible) to create tractable models that provide insight into the system's emergent behaviour.
In this talk, I will present the comprehensive agent-based modelling cycle I employed to analyse the possibility of a green transition in the economy. I will discuss current results obtained from the ABM and, if time permits, address the challenges encountered in constructing and analysing a tractable model.
The unsplittable transshipment problem is a strongly NP-complete network flow problem inspired by the well-studied Single-Source Unsplittable Flow (SSUF) problem. It involves routing a single commodity from sources to sinks in a capacity-constrained network, using at most one path for each source-sink pair. The unsplittable flow problem has applications in network design, logistics, and telecommunications, but its transshipment variant is unexplored in literature.
This talk addresses the unsplittable transshipment problem in directed graphs, proving its strong NP-completeness even under uniform flow conditions (rendering it "harder" than the SSUF problem). We show that converting feasible fractional transshipments to an unsplittable form only requires arc-capacity violations up to the maximum demand of any sink. We propose a generalization of Dinitz Garg Goeman's Algorithm [1] to achieve the aforementioned capacity violations, and restrict the total number of paths to the number of sources plus the number of sinks minus one.
[1] Y. Dinitz, N. Garg, and M. X. Goemans. “On The Single-Source Unsplittable Flow Problem”. In: Combinatorica 19 (1999), pp. 17-41. doi: 10.1007/s004930050043..