BMC2026 Programme
Mon 30th March, 2026
| noon – 2:00pm | Registration and welcome |
| 1:30pm – 2:00pm | Opening @ Abacws/0.01 |
| 2:00pm – 3:00pm | Cristiana de Filippis (Parma) @ Abacws/0.01 |
| “Surfing regularity on nonlinear potentials” (abstract) | |
| 3:00pm – 4:00pm | Sections |
| 4:00pm – 4:30pm | Coffee break |
| 4:30pm – 6:00pm | Sections (continued) |
| 6:00pm - 9:00pm | LMS Social and Drinks Reception |
Tue 31st March, 2026
| 9:00am – 10:00am | Gui-Qiang G. Chen (Oxford) @ Abacws/0.01 |
| “Partial differential equations of mixed type − analysis and connections” (abstract) | |
| 9:00am – 10:00am | Ivan Nourdin (Luxembourg) @ Abacws/2.26 |
| “Quantitative CLT for deep neural networks” (abstract) | |
| 10:00am – 11:00am | Enrico Le Donne (Freiburg) @ Abacws/0.01 |
| “Metric Lie groups” | |
| 10:00am – 11:00am | Soheyla Feyzbakhsh (Imperial) @ Abacws/2.26 |
| “Applications of Bridgeland stability conditions in algebraic geometry” (abstract) | |
| 11:00am – 11:30am | Coffee break |
| 11:30am – 12:30pm | Dennis Gaitsgory (MPIM, Bonn) @ Abacws/0.01 |
| “Deligne-Lusztig theory as trace” (abstract) | |
| 12:30pm – 1:30pm | Lunch |
| 1:30pm – 1:45pm | BMC AGM Meeting @ Abacws/0.01 |
| 1:45pm – 3:00pm | LMS Lecture and Society Meeting: Péter Varjú (Cambridge) @ Abacws/0.01 |
| 3:00pm – 4:00pm | Sections |
| 4:00pm – 4:30pm | Coffee break |
| 4:30pm – 6:00pm | Sections (continued) |
| Evening | Conference dinner |
Wed 1st April, 2026
| 9:00am – 10:00am | Giovanna Citti (Bologna) @ Abacws/0.01 |
| 9:00am – 10:00am | Dustin Clausen (IHES, Paris) @ Abacws/2.26 |
| 10:00am – 11:00am | Daniel Huybrechts (Bonn) @ Abacws/0.01 |
| “Brauer groups and geometry: The period-index conjecture” (abstract) | |
| 10:00am – 11:00am | Luisa Beghin (Sapienza, Rome) @ Abacws/2.26 |
| “Random processes through non-local operators: analytical versus stochastic approaches” (abstract) | |
| 11:00am – 11:30am | Coffee break |
| 11:30am – 12:30pm | Mikhail Kapranov (IPMU, Tokyo) @ Abacws/0.01 |
| “Supersymmetry, differential operators of infinite order and theta-functions” (abstract) | |
| 12:30pm – 2:00pm | Lunch |
| 2:00pm – 3:00pm | Johannes Schmidt-Hieber (Twente) @ Abacws/0.01 |
| “The mathematics behind spiking neural networks” (abstract) | |
| 3:00pm – 4:00pm | Sections |
| 4:00pm – 4:30pm | Coffee break |
| 4:30pm – 6:00pm | Sections (continued) |
| 6:00pm – 7:30pm | Pizza buffet |
| 7:30pm – 8:30pm | Public lecture: Jens Marklof (Bristol) @ Centre for Student Life/2.06 |
| “The Mathematics of Chaos: Predicting the Unpredictable” (abstract) |
Thu 2nd April, 2026
| 9:00am – 10:00am | ICMS Lecture: Yasuyuki Kawahigashi (Tokyo) @ Abacws/0.01 |
|
“Quantum symmetries in operator algebras and
mathematical physics” (abstract) |
|
| 9:00am – 10:00am | Pavel Kurasov (Stockholm) @ Abacws/2.26 |
| “Higher Dimensional Crystallines from Lee-Yang Varieties” (abstract) | |
| 10:00am – 11:00am | Cyril Houdayer (ÉNS, Paris) @ Abacws/0.01 |
| “Lattices, Weyl groups and rigidity of von Neumann algebras” (abstract) | |
| 10:00am – 11:00am | Christoph Schweigert (Hamburg) @ Abacws/2.26 |
| “Skein theory, Frobenius functors and CFT correlators” (abstract) | |
| 11:00am – 11:30am | Coffee break |
| 11:30am – 12:30pm | Yoshiko Ogata (RIMS, Kyoto) @ Abacws/0.01 |
| “Topological order: an operator-algebraic approach” (abstract) | 12:30pm – 1:00pm | Closure @ Abacws/0.01 | 1:30pm – 5:00pm | Extra talks in the Geometry section |
Abstracts
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Luisa Beghin (Sapienza, Rome): Random processes through non-local operators: analytical versus stochastic approaches
We describe two alternative approaches to introducing non-local operators in random models: the analytic approach versus the stochastic one. In the first case, fractional derivatives, in either the classical or generalized sense, appear in place of integer-order derivatives in the partial differential equations that govern the random processes. In the second case, on the other hand, non-local differential and integral operators are introduced directly into the definition of the generalized random process in infinite-dimensional spaces (with various types of measures). Both approaches can lead to models of anomalous diffusions and processes with memory.
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Gui-Qiang G. Chen (Oxford): Partial differential equations of mixed type − analysis and connections
Three of the fundamental types of partial differential equations (PDEs) — elliptic, hyperbolic, and parabolic — arise from the classical classification of linear PDEs. The linear theory for each of these types has been extensively developed. By contrast, many nonlinear PDEs arising in mathematics and the sciences are naturally of mixed type. A deep understanding of such nonlinear PDEs — particularly those of mixed elliptic-hyperbolic type — is essential for solving several longstanding fundamental problems. Notable examples include the multidimensional Riemann problem (formulated by Riemann in 1860 for the one-dimensional case) and related shock reflection/diffraction problems in fluid dynamics for the compressible Euler equations, as well as the isometric embedding problem in differential geometry governed by the Gauss-Codazzi-Ricci system. In this talk, we will present both classical and recent connections between nonlinear PDEs of mixed type and these fundamental problems, ranging from the Riemann problem to isometric embedding. We will then discuss recent developments in the analysis of nonlinear mixed-type PDEs, with an emphasis on unified ideas, approaches, and techniques for addressing such problems. Some further perspectives and open problems in this evolving direction will also be addressed.
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Soheyla Feyzbakhsh (Imperial): Applications of Bridgeland stability conditions in algebraic geometry
After a brief introduction to Bridgeland stability conditions on triangulated categories, I will explain several recent applications in algebraic geometry. These include their role in the Brill–Noether theory of vector bundles as well as in the enumerative geometry of Donaldson–Thomas theory.
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Cristiana de Filippis (Parma): Surfing regularity on nonlinear potentials
The representation formula for the Poisson equation gives an explicit expression of solutions in terms of the data, yielding zero- and first-order pointwise bounds via convolution with appropriate Riesz potentials. The mapping properties of these potentials provide sharp regularity transfer from data to solutions, giving a complete description of the regularity features of solutions. I will outline key aspects of nonlinear potential theory that reproduce this behavior for nonlinear elliptic PDEs, where representation formulae are unavailable, and trace their regularity theory back to that of the Poisson equation up to the \(C^{1}\) level. I will then present a novel potential-theoretic approach, altering a century old paradigm in nonlinear regularity theory, that resolves the longstanding problem of the validity of Schauder theory in nonuniformly elliptic PDEs.
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Dennis Gaitsgory (MPIM, Bonn): Deligne-Lusztig theory as trace
We will use the formalism of (higher) categorical trace to obtain a natural construction of Deligne-Lusztig representations. We will be able to recover a number of know results, and also obtain some new ones: independence of Deligne-Lusztig characters of the parabolic.
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Cyril Houdayer (ÉNS, Paris): Lattices, Weyl groups and rigidity of von Neumann algebras
Connes' rigidity conjecture predicts that the von Neumann algebra of a higher rank lattice should remember the ambient simple Lie group. In this talk, I will explain a recent result showing that the Weyl group of a simple Lie group is an invariant of a natural inclusion of von Neumann algebras attached to the lattice. I will also present a noncommutative analogue of Margulis' factor theorem for higher rank lattices, which gives further insight towards Connes' rigidity conjecture. Based on joint works with A. Ioana and R. Boutonnet.
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Daniel Huybrechts (Bonn): Brauer groups and geometry: The period-index conjecture
Brauer-Severi varieties (so smooth fibrations with projective spaces as fibres) are not Zariski locally trivial. The failure is measured by the associated Brauer class to which two numerical invariants are attached: period and index. The precise relation between the two is unknown but the index is conjectured to be universally bounded by some power of the period. The talk will start with a gentle introduction into the general theory with a survey of things that are known. In the second half I will study the problem for hyperkähler varieties in which case a better bound is expected and in fact can be proved in interesting cases.
- Mikhail Kapranov (IPMU, Tokyo): Quantum symmetries in operator algebras and mathematical physics
Differential operators of infinite order were introduced by M. Sato in 1959. They are infinite series in derivatives with sufficient decay conditions which act on holomorphic functions by sheaf homomorphisms (i.e., without changing the domain of definition). For example, \(\mathrm{exp}(\frac{d}{dx})\), the shift operator, is not allowed but \(\cos(\sqrt{\frac{d}{dx}})\) is.
Starting from 1972, Sato, Kashiwara, Kawai, Takei and others developed a way to prove modularity of functions such as Theta-zero-values by characterizing them via manifestly modular invariant systems of differential operators of infinite order in the modular variables alone. I will present a natural "physical/supersymmetric" framework for this approach. The main phenomenon is that in some cases the odd supersymmetry generators considered "on shell" (i.e., on the space of solution of equations of motion) satisfy even Heisenberg commutation relations.
- Yasuyuki Kawahigashi (Tokyo): Quantum symmetries in operator
algebras and mathematical physics
A group gives a classical notion of symmetry. We have seen a new type of “quantum symmetries” in many different fields in mathematics and physics over the last four decades. I will present recent advances in this area connected to the Jones theory of subfactors, conformal field theory, and two-dimensional condensed matter physics. This is a general talk without any particular prerequisites.
- Pavel Kurasov (Stockholm): Higher Dimensional Crystallines from Lee-Yang Varieties
Current talk is about a new family of aperiodic crystals, which are different from quasicrystals introduced by experimental and theoretical physicists and analysed by mathematicians.
A discrete set is called crystalline, if it is a support of a crystalline measure \[ \mu = \sum_{\lambda \in \Lambda} a_\lambda \delta_\lambda, \quad \hat{\mu} = \sum_{s \in S} b_s \delta_s, \] with all \(a_\lambda = 1\) and possessing additional property, that not only \( \mu \) (and hence \( \hat{\mu} \) are tempered distributions, but also \[ |\hat{\mu}| := \sum_{s \in S} |b_s| \delta_s, \] is tempered.
One-dimensional crystallines can be obtained using stable Lee-Yang polynomials, as it was suggested in our joint paper with P.Sarnak. It was proven by Olevskiii-Ulanovskii and Alon-Cohen-Vinzant that this construction gives all one-dimensional crystallines.
Multidimensional crystallines are discussed in the current talk. It is shown that a rather general family of crystallines in \( \mathbb R^d \) can be constructed using co-dimension \( d \) Lee-Yang varieties in \( \mathbb C^n, \, n > d.\) These complex algebraic varieties are symmetric and avoid certain regions in \( \mathbb C^n \), thus generalising zero sets of Lee-Yang polynomials.
It is shown that such crystallines can be supported by Delaunay almost periodic sets and are genuinely multidimensional in the sense that their restriction to any one-dimensional subspace is not given by a one-dimensional crystalline. To classify all multidimensional crystallines proposed construction has to be modified including singular Lee-Yang varieties.
We show that obtained sets are either periodic, or form aperiodic crystals. Only periodic crystallines formally coincide with quasicrystals.
This is joint work with L. Alon, M. Kummer, C. Vinzant, Y.Meyer, and P.Sarnak.
- Jens Marklof (Bristol):
The Mathematics of Chaos: Predicting the Unpredictable
We live in a chaotic world: from weather forecasts and natural disasters to political developments, it seems often impossible to even make the most basic predictions. In this lecture I will discuss one of the most fundamental mathematical principles behind such unpredictability: the inherent instability of systems with chaotic behaviour that leads to extreme amplification of the smallest errors in the data. In particular, I will explore with you the legendary question “Does the flap of a butterfly’s wings in Brazil set off a tornado in Texas?” (Lorenz 1972) and explain how chaos theory has established the best way of kneading bread dough! By the end of this lecture, I hope to have convinced you of the power of mathematics in the understanding of some of the world’s most complex systems. And although we will never be able to predict the future with complete certainty, we can forecast likelihoods. The more chaotic, the better!
- Ivan Nourdin (Luxembourg): Quantitative
CLT for deep neural networks
I will discuss the asymptotic behavior at initialization of fully connected deep neural networks with Gaussian weights and biases when the widths of the hidden layers go to infinity.
This talk is addressed to a broad mathematical audience. Apart from a basic knowledge of probability theory, no specific prerequisites are required, and all the necessary notions will be introduced progressively throughout the presentation.
This is based on joint work with S. Favaro, B. Hanin, D. Marinucci and G. Peccati.
- Yoshiko Ogata (RIMS, Kyoto): Topological order: an operator-algebraic approach
Quantum many-body physics is a field of physics that investigates macroscopic properties of matter emerging from the collective behavior of many interacting quantum particles. The study of topological order tries to classify phases of matter by introducing equivalence or preorder relations between states of physical interest from a physically motivated point of view. This physical point of view introduces the concept of locality to the problem, a feature that has not been extensively investigated in purely mathematical research. In this talk, I would like to give an overview of this developing area of mathematical physics.
- Johannes Schmidt-Hieber (Twente):
The mathematics behind spiking neural networks
Artificial neural networks are inspired by the functioning of the brain but differ in several key aspects. In biological neural networks, information is encoded in the spiking times of neurons. In this survey talk, we first address the expressiveness of spiking neural networks and derive a universal representation theorem.
Furthermore, it is implausible that biological learning is based on gradient descent. This has prompted researchers to propose various biologically inspired learning procedures. However, these methods lack a solid theoretical foundation. While statistical theory for artificial neural networks has been developed over the past years, the aim now is to extend this theory to biological neural networks, as the future of AI is likely to draw even more inspiration from biology. We will explore the challenges and present some recent theoretical results.
Joint work with Niklas Dexheimer, Sascha Gaudlitz, Shayan Hundrieser, Insung Kong, and Philipp Tuchel.
- Christoph Schweigert (Hamburg):
Skein theory, Frobenius functors and CFT correlators
Skein theory is an efficient tool for the graphical construction of topological field theories and modular functors, based on a given input category \(C\). We show that a Frobenius monoidal functor \(C \rightarrow C\) induces a relation between the associated skein theories. We present a situation where this relation is an equivalence. This turns out to encode information about correlators of two-dimensional conformal field theories.