L2

Drug discovery is slow and expensive, and a growing body of AI work tackles this by training generative models that propose new candidate molecules directly, searching chemical space far faster than a human chemist could. Most of this work has focused on standard small molecules, leaving more specialized but valuable classes underexplored.

Macrocycles are ring-shaped molecules that offer a promising alternative to small-molecule drugs due to their enhanced selectivity and binding affinity against difficult targets. Despite their chemical value, they remain underexplored in generative modeling, likely owing to their scarcity in public datasets and the challenges of enforcing topological constraints in standard deep generative models.

We introduce MacroGuide: Topological Guidance for Macrocycle Generation, a diffusion guidance mechanism that uses Persistent Homology to steer the sampling of pretrained molecular generative models toward the generation of macrocycles, in both unconditional and conditional (protein pocket) settings. At each denoising step, MacroGuide constructs a Vietoris-Rips complex from atomic positions and promotes ring formation by optimizing persistent homology features. Empirically, applying MacroGuide to pretrained diffusion models increases macrocycle generation rates from 1% to 99%, while matching or exceeding state-of-the-art performance on key quality metrics such as chemical validity, diversity, and PoseBusters checks.

Accepted to ICML 2026. Paper: https://arxiv.org/abs/2602.14977

The celebrated additive kinematic formula expresses the mean volume of the Minkowski sum of two compact convex subsets of the Euclidean space placed at random. What about non convex subsets? What about other Lie groups than the Euclidean space? In a joint work with Andreas Bernig, we prove additive kinematic formulas for compact subanalytic sets of the Euclidean space and of the 3-sphere. The key is to generalize the Minkowski sum of convex bodies by a notion of convolution of subanalytic sets introduced by Schapira in the late 80s using Euler characteristic computations. The above will of course be an excuse to discuss integral geometric formulas and constructible functions.

This session is aimed at first-year undergraduates preparing for Prelims exams. A panel of lecturers and current students will share key advice on exam technique and revision strategies, offering practical tips from their own experience.

The talk gives some survey about recent applications of finitely additive measures to Lebesgue integrable functions. After a short introduction to such measures and related integrals, purely finitely additive measures are of particular interest. Special examples are given and, as a first application, an integral representation for the precise representative of Lebesgue integrable functions is provided. Then, based on a general approach to traces, a new version of the Gauss-Green formula is introduced, where neither a pointwise trace nor a pointwise normal is needed on the boundary. This allows e.g. the treatment of inner boundaries and of concentrations on the boundary. A second boundary integral is used to handle singularities that hadnot been accessible before. Finally, weak versions of differentiability for Lebesgue integrable functions are discussed, a mean value formula for a class of Sobolev functions is given, and a new approach to the generalized derivatives in the sense of Clarke is provided.

The Hitchin equations are an integrable system in two-dimensions that plays a variety of important roles across mathematics and physics and this talk will start with some of this motivation.  It will go on to discuss how the 4d Chern-Simons of Costello, Witten and Yamazaki fits into ideas from  30-40 years ago that sought to unify the study of integrable systems via the study of the self-duality equations and their twistor constructions.  In particular 4d Chern-Simons provides a uniform approach to 2d integrable systems and their canonical structures.  The Hitchin equations have been missing in this approach and this talk will explain I will explain how Hitchin equations are incorporated with reductions to Toda and Sine Gordon, and  gives new approaches to understanding canonical strucures associated with these equations.  This talk is based on joint work with Roland Bittleston and Faroogh Moosavian https://arxiv.org/abs/2601.05309.

 Hydrodynamics provides a universal low-energy effective description of interacting many-body systems. Traditionally, it is formulated in terms of equations of motion derived from the relevant conservation laws. However, this classical framework neglects fluctuations of hydrodynamic observables required by the fluctuation–dissipation theorem (FDT). The Schwinger–Keldysh effective field theory (SK EFT) offers a Wilsonian, action-based formulation of hydrodynamics that systematically incorporates such fluctuations. In this approach, the effective action is generically non-unitary (complex), encoding macroscopic dissipation, while the FDT is implemented through a discrete Kubo–Martin–Schwinger (KMS) symmetry. This symmetry also underlies the emergence of the second law of thermodynamics within hydrodynamics.