Past

How can it be that so many clever, competent and capable people can feel that they are just one step away from being exposed as a complete fraud? Despite evidence that they are performing well they can still have that lurking fear that at any moment someone is going to tap them on the shoulder and say "We need to have a chat". If you've ever felt like this, or you feel like this right now, then this Friday@2 session might be of interest to you. We'll explore what "Imposter Feelings" are, why we get them and steps you can start to take to help yourself and others. This event is likely to be of interest to undergraduates and MSc students at all stages. 

This is a report on the ongoing joint project with Giovanni Felder and David Kazhdan. I'll describe a conjectural way to set up the integration of the superstring measure on the moduli space of supercurves, including a brief review of the necessary supergeometry. The main theorem is that this setup works for genus 2 with no punctures.

In ’95 Lusztig gave a local Langlands correspondence for unramified representations of inner to split adjoint groups combining many deep results from type theory and geometric representation theory. In this talk I will present a gentle reformulation of his construction revealing some interesting new structures, and with a view toward proving functoriality results in this framework. 

In ’95 Lusztig gave a local Langlands correspondence for unramified representations of inner to split adjoint groups combining many deep results from type theory and geometric representation theory. In this talk, I will present a gentle reformulation of his construction revealing some interesting new structures, and with a view toward proving functoriality results in this framework. 

This seminar is organised jointly with the Junior Algebra and Representation Theory Seminar - all are very welcome!

Underlying many biological models are chemical reaction networks (CRNs), and identifying allowed and forbidden dynamics in reaction networks may 
give insight into biological mechanisms. Algebraic approaches have been important in several recent developments. For example, computational 
algebra has helped us characterise all small mass action CRNs admitting certain bifurcations; allowed us to find interesting and surprising 
examples and counterexamples; and suggested a number of conjectures.   Progress generally involves an interaction between analysis and 
computation: on the one hand, theorems which recast apparently difficult questions about dynamics as (relatively tractable) algebraic problems; 
and on the other, computations which provide insight into deeper theoretical questions. I'll present some results, examples, and open 
questions, focussing on two domains of CRN theory: the study of local bifurcations, and the study of multistationarity.

The (Local) Lifting Property ((L)LP) is introduced by Kirchberg and deals with lifting completely positive maps. We will discuss various examples, characterizations, and closure properties of the (L)LP and, if time permits, connections with some other lifting properties of C*-algebras.  Joint work with Dominic Enders.

A number of results on classical problems in analytic number theory rely on bounds for multilinear forms of Kloosterman sums, which in turn use deep inputs from the spectral theory of automorphic forms. We’ll discuss our recent work available at arxiv.org/abs/2404.04239, which uses this interplay between counting problems, exponential sums, and automorphic forms to improve results on the greatest prime factor of $n^2+1$, and on the exponents of distribution of primes and smooth numbers in arithmetic progressions.
The key ingredient in this work are certain “large sieve inequalities” for exceptional Maass forms, which improve classical results of Deshouillers-Iwaniec in special settings. These act as on-average substitutes for Selberg’s eigenvalue conjecture, narrowing (and sometimes completely closing) the gap between previous conditional and unconditional results.

Large Language Models (LLMs) have demonstrated impressive achievements. However, recent research has shown that their deeper layers often contribute minimally, with effectiveness diminishing as layer depth increases. This pattern presents significant opportunities for model compression. 

In the first part of this seminar, we will explore how this phenomenon can be harnessed to improve the efficiency of LLM compression and parameter-efficient fine-tuning. Despite these opportunities, the underutilization of deeper layers leads to inefficiencies, wasting resources that could be better used to enhance model performance. 

The second part of the talk will address the root cause of this ineffectiveness in deeper layers and propose a solution. We identify the issue as stemming from the prevalent use of Pre-Layer Normalization (Pre-LN) and introduce Mix-Layer Normalization (Mix-LN) with combined Pre-LN and Post-LN as a new approach to mitigate this training deficiency.

Multicomponent flows, i.e. mixtures, can be modeled effectively using the Onsager-Stefan-Maxwell (OSM) equations. The OSM equations can account for a wide variety of phenomena such as diffusive, convective, non-ideal mixing, thermal, pressure and electrochemical effects for steady and transient multicomponent flows. I will first introduce the general OSM framework and a finite element discretisation for multicomponent diffusion of ideal gasses. Then I will show two ways of preconditioning the multicomponent diffusion problem for various boundary conditions. Time permitting, I will also discuss how this can be extended to the non-ideal, thermal, and nonisobaric settings.

The Brunn-Minkowski inequality gives a lower bound on the volume of the set of midpoints of line segments joining two sets. On a Riemannian manifold, line segments are replaced by geodesic segments, and the Brunn-Minkowski inequality characterizes manifolds with nonnegative Ricci curvature. I will present a generalization of the Riemannian Brunn-Minkowski inequality where geodesics are replaced by magnetic geodesics, which are minimizers of a functional given by length minus the integral of a fixed one-form on the manifold. The Brunn-Minkowski inequality is then equivalent to nonnegativity of a suitably defined magnetic Ricci curvature. More generally, I will present a magnetic version of the Borell-Brascamp-Lieb inequality of Cordero-Erausquin, McCann and Schmuckenschläger. The proof uses the needle decomposition technique.

How should we interpret past mathematicians who may use the same vocabulary as us but with different meanings, or whose philosophical outlooks differ from ours? Errors aside, it is often assumed that past mathematicians largely made true claims—but what exactly justifies that assumption?

In this talk, we will explore these questions through general philosophical considerations and three case studies: 19th-century analysis, 18th-century geometry, and 19th-century matricial algebra.  In each case, we encounter a significant challenge to supposing that the mathematicians in question made true claims. We will show how these challenges can be addressed and overcome.

In 1911, Otto Toeplitz posed the intriguing "Square Peg Problem," asking whether every Jordan curve admits an inscribed square. Despite over a century of study, the problem remains unsolved in its full generality. However, significant progress has been made over the years. In this talk, we explore recent advancements by Andrew Lobb and Joshua Greene, who approach the problem through the lens of Lagrangian Floer homology. Specifically, we outline a proof of their result: every smooth Jordan curve inscribes every rectangle up to similarity.

I will present TeXmacs (www.texmacs.org), a document preparation system with structured editing and high quality typography, designed to create technical documents. 

For more details see https://mgubi.github.io/docs/programming.html

Motivated by a recent experiment on a superconducting quantum
information processor, I will discuss the Floquet quantum Ising model in
the presence of integrability- and symmetry-breaking random fields. The
talk will focus on the relation between boundary spin correlations,
spectral pairings, and effects of the random fields. If time permits, I
will also touch upon self-similarity in the dynamic phase diagram of
Fibonacci-driven quantum Ising models.
 

I will give a light introduction to the concept of a quantum expander, which is an analogue of an expander graph that arises in quantum information theory.  Most examples of quantum expanders that appear in the quantum information literature are obtained by random matrix techniques.  I will explain another, more algebraic approach to constructing quantum expanders, which is based on using actions and representations of discrete quantum groups with Kazhdan's property (T).  This is joint work with Eric Culf (U Waterloo) and Matthijs Vernooij (TU Delft).   

In a recent breakthrough Campos, Griffiths, Morris and Sahasrabudhe obtained the first exponential improvement of the upper bound on the classical Ramsey numbers since 1935. I will outline a reinterpretation of their proof, replacing the underlying book algorithm with a simple inductive statement. In particular, I will present a complete proof of an improved upper bound on the off-diagonal Ramsey numbers and describe the main steps involved in improving their upper bound for the diagonal Ramsey numbers to $R(k,k)\le(3.8)^k$ for sufficiently large $k$.

Based on joint work with Parth Gupta, Ndiame Ndiaye, and Louis Wei.

I will present a joint work with Thang Nguyen where we show that there exists a quasi-isometric embedding of the product of n copies of the hyperbolic plane into any symmetric space of non-compact type of rank n, and there exists a bi-Lipschitz embedding of the product of n copies of the 3-regular tree into any thick Euclidean building of rank n. This extends a previous result of Fisher--Whyte. The proof is purely geometrical, and the result also applies to the non Bruhat--Tits buildings. I will start by describing the objects and the embeddings, and then give a detailed sketch of the proof in rank 2.

Let $(V(u))$ be a branching random walk and $(\eta(u))$ be i.i.d marks on the vertices. To each path $\xi$ of the tree, we associate the discounted sum $D(\xi)$ which is the sum of the $\exp(V(u))\eta_u$ along the path. We study conditions under which $\sup_\xi D(\xi)$ is finite, answering an open question of Aldous and Bandyopadhyay. We will see that this problem is related to the study of the local time process of the branching random walk along a path. It is a joint work with Yueyun Hu and Zhan Shi.

Suppose a finite group satisfies the following property: If you take two random elements, then with probability bigger than 5/8 they commute. Then this group is commutative. 

Starting from this well-known result, it is natural to ask: Do similar results hold for other laws (p-groups, nilpotent groups...)? Are there analogous results for infinite groups? Are there phenomena specific to the infinite setup? 

We will survey known and new results in this area. New results are joint with Gideon Amir, Maria Gerasimova and Gady Kozma.

Networks provide a powerful language to model and analyse interconnected systems. Their building blocks are  edges, which can  then be combined to form walks and paths, and thus define indirect relations between distant nodes and model flows across the system. In a traditional setting, network models are first-order, in the sense that flow across nodes is made of independent sequences of transitions. However, real-world systems often exhibit higher-order dependencies, requiring more sophisticated models. Here, we propose a variable-order network model that captures memory effects by interpolating between first- and second-order representations. Our method identifies latent modes that explain second-order behaviors, avoiding overfitting through a Bayesian prior. We introduce an interpretable measure to balance model size and description quality, allowing for efficient, scalable processing of large sequence data. We demonstrate that our model captures key memory effects with minimal state nodes, providing new insights beyond traditional first-order models and avoiding the computational costs of existing higher-order models.

In this talk I will explain how the size of the Einstein-Rosen (ER) bridge dual to the Double Scaled SYK (DSSYK) model saturates at late times because of finiteness of the underlying quantum Hilbert space.  I will extend recent work implying that the ER bridge size equals the spread complexity of the dual DSSYK theory with an appropriate initial state.  This work shows that the auxiliary "chord basis'' used to solve the DSSYK theory is the physical Krylov basis of the spreading quantum state.  The ER bridge saturation follows from the vanishing of the Lanczos spectrum, derived by methods from Random Matrix Theory (RMT).