Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

 

Wed, 28 Sep 2022 09:00 -
Sun, 08 Oct 2023 17:00
Mathematical Institute

Cascading Principles - a major mathematically inspired exhibition by Conrad Shawcross

Further Information

Oxford Mathematics is delighted to be hosting one of the largest exhibitions by the artist Conrad Shawcross in the UK. The exhibition, Cascading Principles: Expansions within Geometry, Philosophy, and Interference, brings together nearly 40 of Conrad's mathematically inspired works from the past seventeen years. Rather than in a gallery, they are placed in the working environment of the practitioners of the subject that inspired them, namely mathematics.

Conrad Shawcross models scientific thought and reasoning within his practice. Drawn to mathematics, physics, and philosophy from the early stages of his artistic career, Shawcross combines these disciplines in his work. He places a strong emphasis on the nature of matter, and on the relativity of gravity, entropy, and the nature of time itself. Like a scientist working in a laboratory, he conceives each work as an experiment. Modularity is key to his process and many works are built from a single essential unit or building block. If an atom or electron is a basic unit for physicists, his unit is the tetrahedron.

Unlike other shapes, a tetrahedron cannot tessellate with itself. It cannot cover or form a surface through its repetition - one tetrahedron is unable to fit together with others of its kind. Whilst other shapes can sit alongside one another without creating gaps or overlapping, tetrahedrons cannot resolve in this way. Shawcross’ Schisms are a perfect demonstration of this failure to tessellate. They bring twenty tetrahedrons together to form a sphere, which results in a deep crack and ruptures that permeate its surface. This failure of its geometry means that it cannot succeed as a scientific model, but it is this very failure that allows it to succeed as an art work, the cracks full of broad and potent implications.

The show includes all Conrad's manifold geometric and philosophical investigations into this curious, four-surfaced, triangular prism to date. These include the Paradigms, the Lattice Cubes, the Fractures, the Schisms, and The Dappled Light of the Sun. The latter was first shown in the courtyard of the Royal Academy and subsequently travelled all across the world, from east to west, China to America.

The show also contains the four Beacons. Activated like a stained-glass window by the light of the sun, they are composed of two coloured, perforated disks moving in counter rotation to one another, patterning the light through the non-repeating pattern of holes, and conveying a message using semaphoric language. These works are studies for the Ramsgate Beacons commission in Kent, as part of Pioneering Places East Kent.

The exhibition Cascading Principles: Expansions within Geometry, Philosophy, and Interference is curated by Fatoş Üstek, and is organised in collaboration with Oxford Mathematics. 

The exhibition is open 9am-5pm, Monday to Friday. Some of the works are in the private part of the building and we shall be arranging regular tours of that area. If you wish to join a tour please email @email.

The exhibition runs until 8 October 2023. You can see and find out more here.

The first of the four public talks about the exhibition (featuring Conrad himself) took place on 23 February. You can watch a recording of the first lecture here.

The exhibition is generously supported by our longstanding partner XTX Markets.

Images clockwise from top left of Schism, Fracture, Axiom and Paradigm

Schism Fracture

Axiom Paradigm

Tue, 28 Mar 2023

14:00 - 15:00
C4

Mixed Hodge modules and real groups

Dougal Davis
(University of Melbourne)
Abstract

I will explain an ongoing program, joint with Kari Vilonen, that aims to study unitary representations of real reductive Lie groups using mixed Hodge modules on flag varieties. The program revolves around a conjecture of Schmid and Vilonen that natural filtrations coming from the geometry of flag varieties control the signatures of Hermitian forms on real group representations. This conjecture is expected to facilitate new progress on the decades-old problem of determining the set of unitary irreducible representations by placing it in a more conceptual context. Our results to date centre around the interaction of Hodge theory with the unitarity algorithm of Adams, van Leeuwen, Trapa, and Vogan, which calculates the signature of a canonical Hermitian form on an arbitrary representation by reducing to the case of tempered representations using deformations and wall crossing. Our results include a Hodge-theoretic proof of the ALTV wall crossing formula as a consequence of a more refined result and a verification of the Schmid-Vilonen conjecture for tempered representations.

Tue, 18 Apr 2023

14:00 - 15:00
L6

Modular Hecke algebras and Galois representations

Tobias Schmidt
(University of Rennes)
Abstract

Let F be a p-adic local field and let G be a connected split reductive group over F. Let H be the pro-p Iwahori-Hecke algebra of the p-adic group G(F), with coefficients in an algebraically closed field k of characteristic p. The module theory over H (or a certain derived version thereof) is of considerable interest in the so-called mod p local Langlands program for G(F), whose aim is to relate the smooth modular representation theory of G(F) to modular representations of the absolute Galois group of F. In this talk, we explain a possible construction of a certain moduli space for those Galois representations into the Langlands dual group of G over k which are semisimple. We then relate this space to the geometry of H. This is work in progress with Cédric Pépin.

Wed, 19 Apr 2023

16:00 - 17:00
C1

TBC

Ruy Exel
(Federal University of Santa Catarina)
Abstract

to follow

Mon, 24 Apr 2023

14:00 - 15:00
L4

Fundamental limits of generative AI

Helmut Bölcskei
(ETH Zurich)
Abstract


Generative AI has seen tremendous successes recently, most notably the chatbot ChatGPT and the DALLE2 software creating realistic images and artwork from text descriptions. Underlying these and other generative AI systems are usually neural networks trained to produce text, images, audio, or video from text inputs. The aim of this talk is to develop an understanding of the fundamental capabilities of generative neural networks. Specifically and mathematically speaking, we consider the realization of high-dimensional random vectors from one-dimensional random variables through deep neural networks. The resulting random vectors follow prescribed conditional probability distributions, where the conditioning represents the text input of the generative system and its output can be text, images, audio, or video. It is shown that every d-dimensional probability distribution can be generated through deep ReLU networks out of a 1-dimensional uniform input distribution. What is more, this is possible without incurring a cost—in terms of approximation error as measured in Wasserstein-distance—relative to generating the d-dimensional target distribution from d independent random variables. This is enabled by a space-filling approach which realizes a Wasserstein-optimal transport map and elicits the importance of network depth in driving the Wasserstein distance between the target distribution and its neural network approximation to zero. Finally, we show that the number of bits needed to encode the corresponding generative networks equals the fundamental limit for encoding probability distributions (by any method) as dictated by quantization theory according to Graf and Luschgy. This result also characterizes the minimum amount of information that needs to be extracted from training data so as to be able to generate a desired output at a prescribed accuracy and establishes that generative ReLU networks can attain this minimum.

This is joint work with D. Perekrestenko and L. Eberhard



 

Tue, 25 Apr 2023

14:00 - 15:00
L6

TBC

Misha Feigin
(University of Glasgow)
Abstract

to follow

Thu, 27 Apr 2023

14:00 - 15:00
Lecture Room 3

TBA

(a talk hosted by Rutherford Appleton Laboratory)
Abstract

TBA

Thu, 27 Apr 2023
14:00

The geometry of the conformal manifolds

Maria Nocchi
Further Information

Junior Strings is a seminar series where DPhil students present topics of common interest that do not necessarily overlap with their own research area. This is primarily aimed at PhD students and post-docs but everyone is welcome.

Fri, 28 Apr 2023

14:00 - 15:00
L3

Stochastic modeling of neurotransmission dynamics

Dr Stefanie Winkelmann
(Zuse Institute Berlin)
Abstract

Abstract: Neurotransmission at chemical synapses relies on the calcium-induced fusion of synaptic vesicles with the presynaptic membrane. The distance of the vesicle to the calcium channels determines the fusion probability and consequently the postsynaptic signal. After a fusion event, both the release site and the vesicle undergo a recovery process before becoming available for reuse again. For all these process components, stochastic effects are widely recognized to play an important role. In this talk, I will present our recent efforts on how to describe and structurally understand neurotransmission dynamics using stochastic modeling approaches. Starting with a linear reaction scheme, a method to directly compute the exact first- and second-order moments of the filtered output signal is proposedFor a modification of the model including explicit recovery steps, the stochastic dynamics are compared to the mean-field approximation in terms of reaction rate equations. Finally, we reflect on spatial extensions of the model, as well as on their approximation by hybrid methods.

References:

A. Ernst, C. Schütte, S. Sigrist, S. Winkelmann. Mathematical Biosciences343, 108760, 2022.

- A. Ernst, N. Unger, C. Schütte, A. Walter, S. Winkelmann. Under Review. https://arxiv.org/abs/2302.01635

 

Tue, 02 May 2023
14:00

TBA

Boris Andrews
Abstract

Placeholder entry; dates+time TBC. 

Tue, 02 May 2023

14:00 - 15:00
L6

TBC

Mark Wildon
(Royal Holloway, University of London)
Abstract

to follow

Tue, 02 May 2023
14:30

TBA

Aaron Baier-Reinio
Abstract

Placeholder entry; date+time to be determined and subject to change. 

Tue, 02 May 2023

16:00 - 17:00
C1

TBC

Siegfried Echterhoff
(University of Münster)
Abstract

to follow

Thu, 04 May 2023

12:00 - 13:00
L1

Can we tailor the behavior of flexible sheets in flows by adding cuts or folds?

Sophie Ramananarivo
(Ecole Polytechnique)
Abstract

Lightweight compliant surfaces are commonly used as roofs (awnings), filtration systems or propulsive appendages, that operate in a fluid environment. Their flexibility allows for shape to change in fluid flows, to better endure harsh or fluctuating conditions, or enhance flight performance of insect wings for example. The way the structure deforms is however key to fulfill its function, prompting the need for control levers. In this talk, we will consider two ways to tailor the deformation of surfaces in a flow, making use of the properties of origami (folded sheet) and kirigami (sheet with a network of cuts). Previous literature showed that the substructure of folds or cuts allows for sophisticated shape morphing, and produces tunable mechanical properties. We will discuss how those original features impact the way the structure interacts with a flow, through combined experiments and theory. We will notably show that a sheet with a symmetric cutting pattern can produce an asymmetric deformation, and study the underlying fluid-structure couplings to further program shape morphing through the cuts arrangement. We will also show that extreme shape reconfiguration through origami folding can cap fluid drag.

Thu, 04 May 2023

14:00 - 15:00
L3

TBA

Bjorn Stinner
(University of Warwick)
Abstract

TBA

Thu, 04 May 2023

16:00 - 17:00
C1

TBC

Daniel Drimbe
(KU Leuven)
Abstract

to follow

Thu, 04 May 2023
17:00
L3

Non-Additive Geometry and Frobenius Correspondences

Shai Haran
(Technion – Israel Institute of Technology)
Abstract

The usual language of algebraic geometry is not appropriate for Arithmetical geometry: addition is singular at the real prime. We developed two languages that overcome this problem: one replace rings by the collection of “vectors” or by bi-operads and another based on “matrices” or props. These are the two languages of [Har17], but we omit the involutions which brings considerable simplifications. Once one understands the delicate commutativity condition one can proceed following Grothendieck footsteps exactly. The square matrices, when viewed up to conjugation, give us new commutative rings with Frobenius endomorphisms.

Fri, 05 May 2023

14:00 - 15:00
Virtual

Data-driven protein design and molecular latent space simulators

Professor Andrew Ferguson
(Pritzker School of Molecular Engineering University of Chicago)
Abstract

Data-driven modeling and deep learning present powerful tools that are opening up new paradigms and opportunities in the understanding, discovery, and design of soft and biological materials. I will describe our recent applications of deep representational learning to expose the sequence-function relationship within homologous protein families and to use these principles for the data-driven design and experimental testing of synthetic proteins with elevated function. I will then describe an approach based on latent space simulators to learn ultra-fast surrogate models of protein folding and biomolecular assembly by stacking three specialized deep learning networks to (i) encode a molecular system into a slow latent space, (ii) propagate dynamics in this latent space, and (iii) generatively decode a synthetic molecular trajectory.

Tue, 09 May 2023

14:00 - 15:00
L6

TBC

Dinakar Muthiah
(University of Glasgow)
Abstract

to follow

Tue, 09 May 2023
15:30
C4

Multivalued Dir-Minimizing Functions

Dr Immanuel Ben Porat
(University of Oxford)
Further Information

The course will serve as an introduction to the theory of multivalued Dir-minimizing functions, which can be viewed as harmonic functions which attain multiple values at each point.

Aimed at Postgraduate students interested in geometric measure theory and its link with elliptic PDEs, a solid knowledge of functional analysis and Sobolev spaces, acquaintance with variational
methods in PDEs, and some basic geometric measure theory are recommended.

Sessions led by  Dr Immanuel Ben Porat will take place on

09 May 2023 15:30 - 17:30 C4

16 May 2023 15:30 - 17:30 C4

23 May 2023 15:30 - 17:30 C4

30 May 2023 15:30 - 17:30 C4

Should you be interested in taking part in the course, please send an email to @email.

Abstract

COURSE_PROPOSAL (12).pdf

The space of unordered tuples. The notion of differentiability and the theory of metric Sobolev in the context of multi-valued functions. Multivalued maximum principle and Holder regularity. Estimates on the Hausdorff dimension of the singular set of Dir-minimizing functions. If time permits: mass minimizing currents and their link with Dir-minimizers. 

Tue, 09 May 2023

16:00 - 17:00
C1

TBC

Mahsa Naraghi
(University of Paris - Sorbonne)
Abstract

to follow

Thu, 11 May 2023
12:00
L1

TBC

Sébastien Neukirch
(Sorbonne Jean Le Rond d’Alembert Lab)
Thu, 11 May 2023

14:00 - 15:00
Lecture Room 3

TBA

Estelle Massart
(UC Louvain)
Fri, 12 May 2023

14:00 - 15:00
L3

To be announced

Prof Deirdre Hollingsworth
(Big Data Institute Nuffield Department of Medicine University of Oxford)
Mon, 15 May 2023

14:00 - 15:00
Lecture Room 6

TBC

Dr Lisa Maria Kreusser
Abstract

TBC