# Research Seminar

The IOL Seminar and Lecture Series at the Zuse Institute Berlin serves to bring together researchers presenting their latest work and to organize tutorial lectures on valuable topics not typically covered in graduate coursework. Presentations usually take place on Wednesday afternoons in ZIB's Seminar Room 2006.

For more information, please contact Sai Nagarajan, Kartikey Sharma, or Zev Woodstock.

For talks before year 2024, see 2022–2023 and 2019–2021.

**Carl Yerger**
– Davidson College

@ ZIB, Room 2005 (Lecture hall)

**Title.**
*Ramsey Theory on the Integer Grid: The "L"-Problem*

**Abstract.**

This talk will begin with a brief introduction to classical Ramsey theory (whose main idea is that complete disorder is impossible) and a discussion of a few well-known results. No specialized background knowledge in combinatorics is required for this talk. Then joint work with Will Smith from University of South Carolina (formerly Davidson) on a Ramsey theory problem based on the integer grid will be presented. Specifically, the L-theorem (an easy corollary of the Gallai-Witt theorem) states that for any integer k, there exists some n such that a k-colored n by n grid must contain a monochromatic "L" (a series of points of the form (i, j), (i, j+t), and (i+t, j+t) for some positive integer t. In this talk, we will investigate the upper bound for the smallest integer n such that a 3-colored n by n integer grid is guaranteed to contain a monochromatic L. We use various methods, such as counting intervals on the main diagonal, to improve the upper bound from 2593 to 493. For the lower bound, we match the lower bound of 21 generated by Canacki et al. (2023) and discuss possible improvements.

**Jobst Heitzig**
– Potsdam Institute for Climate Research

**Title.**
*Social Choice for AI Ethics and Safety*

**Abstract.**

Many recent advances in the field of AI, including tools such as ChatGPT, rely on the training of foundation models. Foundation models are fine-tuned to avoid unsafe or otherwise problematic behavior, so that, for example, they refuse to comply with requests for help with committing crimes, or with producing racist text. One approach to fine-tuning, called reinforcement learning from human feedback, learns from humans’ expressed preferences over multiple outputs. Another approach is constitutional AI, in which the input from humans is a list of high-level principles. But which humans get to provide the feedback or principles? And how is their potentially diverging input aggregated into consistent data about “collective” preferences or otherwise used to make collective choices about model behavior? In this talk, I argue that the field of social choice is well positioned to address these questions, and discuss ways forward for this agenda, drawing on discussions in a recent workshop on Social Choice for AI Ethics and Safety held in Berkeley, CA, USA in December 2023.

**Sophie Huiberts**
– Clermont Auvergne University

**Title.**
*Open problems about the simplex method*

**Abstract.**

The simplex method is a very efficient algorithm. In this talk we see a few of the state-of-the-art theories for explaining this observation. We will discuss what it takes for a mathematical model to explain an algorithm’s qualities, and whether existing theories meet this bar. Following this, we will question what the simplex method is and if the theoretician’s simplex method is the same algorithm as the practitioner’s simplex method.

**Moritz Link**
– University of Konstanz

**Title.**
*Multiobjective mixed-integer nonlinear optimization with application to energy supply networks*

**Abstract.**

In light of the ongoing developments in the climate crisis, it is necessary to consider factors beyond the sole economic perspective in energy supply network planning. This gives rise to a classical multiobjective optimization problem involving conflicting objective functions. The presence of choices in the model, coupled with the consideration of stationary flow equations, results in an opti mization problem with a mixed-integer nonlinear structure. Following a short introduction of some model-specific details and arising challenges, we present a novel method for computing an enclosure of the nondominated set of such prob lems. We prove finite convergence and demonstrate its effectiveness through numerical experiments. We conclude by offering a preview of ongoing extensions of this work.

**Andreas Tillmann**
– TU Braunschweig

@ ZIB, Room 4027

**Title.**
*MIP and ML approaches to matrix sparsification*

**Abstract.**

Sparsity of matrices can be exploited, in particular, to speed up algorithms in various applications, e.g., in linear system solvers or second-order optimization schemes. This motivates to consider the matrix sparsification problem, in which we seek an equivalent (column-space preserving) representation of a given matrix with as few nonzero entries as possible. We derive sequential solution approaches based on bilinear and linear mixed-integer programs, respectively, and point out connections to certain machine learning tasks. One particular problem appears as a subproblem or special case in both these approaches: Finding a sparsest nonzero vector in the nullspace of a matrix. We will outline how a dedicated branch-and-cut method for this problem can be utilized in the envisioned matrix sparsification algorithms, and touch upon some open questions and challenges of our ongoing work