Edmund R. Michalik Distinguished Lecture Series
On October 25, 2024, Professor Heather Macbeth, who is an assistant professor in the Department of Mathematics at Fordham University gave the 2024 Edmund R. Michalik Distinguished Lecture in the Mathematical Sciences to a full room of students and faculty from Pitt, Carnegie Mellon, and Duquesne. After decades of work by mathematicians called "theoretical computer scientists", computer systems for formalization -- expressing proofs as strict chains of logical reasoning, down to the axioms -- are now powerful and user-friendly enough for modern research mathematics. And indeed, instances of hot-off-the-press theorems being formalized are starting to accumulate, including Hales' proof of the Kepler conjecture, Clausen-Scholze's work on condensed mathematics, and Gowers-Green-Manners-Tao's proof of the Polynomial Freiman-Ruzsa conjecture.
These developments suggest new paradigms for the interaction of mathematics and computation. Computer formalization systems (called ITPs, for "interactive theorem provers") can explain to us what our "abstract nonsense" means, and force us to explain to them what we mean by "routine" proofs; in both cases an implicit algorithm is made explicit. ITPs are the ideal vehicle for very computational proofs -- so much so that the line between "brute force" proofs and "principled" proofs begins to blur. And seemingly in contrast to this, ITPs may nudge us toward a different style of mathematical discovery, less reasoned and more intuitive.
Recent Workshops at the Pitt Mathematical Research Center
Pittsburgh Links among Analysis and Number Theory
The purpose of the conference is to bring together representatives of two disciplines with multiple points of interface: number theory and analysis. Click here for more information.
Recent Advances on Hyperbolic PDEs and Applications
Mini-Workshop on Combinatorial Algebraic Geometry
The themes of the workshop are toric geometry, convex polytopes, and matroids. Click here for abstract information.
Mathematical Models and Numerical Methods for Multiphysics Systems
The conference aims to bring together experts from different communities in which computational models for multiphysics systems are employed. Multiphysics systems model the physical interactions between two or more media, such as couplings of fluid flows, rigid or deformable porous media, and elastic structures. Typical examples are coupling of free fluid and porous media flows, fluid--structure interaction, and fluid--poroelastic structure interaction. Applications of interest include climate modeling, interaction of surface and subsurface hydrological systems, fluid flows through fractured or deformable aquifers or reservoirs, evolution of soil structures, arterial flows, perfusion of living tissues, and organ modeling, such as the heart, lungs, and brain. The work presented at the conference will cover both rigorous mathematical and numerical analysis and applications to cutting-edge problems.
The main topics of the conference include the following:
- Development and analysis of mathematical models for multiphysics systems
- Discretization methods for multiphysics systems
- Solution strategies for multiphysics systems
- Applications
Workshop on Generalized Galois Tukey Connections and Topology
This workshop is devoted to the interaction between Galois-Tukey theory and set theoretic topology. Generalized Galois-Tukey morphisms were introduced and studied by Vojtas, Fremlin, Blass and others to illuminate Cichon's diagram and other relationships between cardinal characteristics of the continuum. Recently the same ideas of focusing on underlying relations, and their morphisms, has been shown to been highly effective in set theoretic topology.