Mikefest: A conference in honor of Michael Douglas' 60th birthday

9 mai 2022, 09:00 → 13 mai 2022, 17:20 Europe/Paris

Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Organized by Costas Bachas (LPENS), Semyon Klevtsov (Univ. Strasbourg), Nikita Nekrasov (Simons Center for Geometry and Physics & Stony Brook) and Emmanuel Ullmo (IHES), the "MikeFest: a conference in honor of Michael Douglas" will take place from May 9 to 13, 2022.

Registration until: May 3, 2022.

We are organizing a conference at the IHES on the occasion of Michael R. Douglas' 60th birthday.

Mike has a long association with IHES, as a visiting professor in 2000-2008 (Louis Michel Chair), by leading the US-based fundraising effort, and as a president and chairman of the Friends of IHES in 2013-2021.

The conference will cover the topics on which Mike has worked and made profound contributions: string theory, matrix models, physical mathematics, and machine learning.

Covid-19 regulations: seats in the conference center are limited to 70 people. The conference will also be available via Zoom.

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Invited speakers:

• Vijay Balasubramanian, Univ. of Pennsylvania
• Alexander Belavin, Independent Univ. Moscow (TBC)
• Ilka Brunner, Univ. München
• Alain Connes, IHES & Collège de France
• Frederik Denef, Columbia Univ.
• Bartomeu Fiol, Univ. de Barcelona
• Jaume Gomis, Perimeter Institute (TBC)
• Sasha Gorsky, IITP RAS, MIPT
• Chris Hull, Imperial College
• Shamit Kachru, Stanford Univ.
• Volodya Kazakov, LPENS
• Maxim Kontsevich, IHES
• Patrick Massot, LMO - Univ. Paris-Saclay
• Luca Mazzucato*, Univ. of Oregon
• David McAllester, Toyota Tech. Inst. Chicago (TTIC)*
• Liam McAllister, Cornell Univ.
• Greg Moore*, Rutgers Univ.
• Rémi Monasson, LPENS
• Eliezer Rabinovici, Hebrew Univ. of Jerusalem
• John Schwarz, CALTECH
• Nathan Seiberg*, IAS
• Steve Shenker*, Stanford Univ.
• Eva Silverstein*, Stanford Univ.
• Christian Szegedy, Google Research
• Washington Taylor*, MIT
• Alessandro Tomasiello, Univ. Degli Studi Di Milano Bicocca
• Josef Urban, CIIRC
• Steve Zelditch*, Northwestern Univ.

* remote talks

HotelsAreaEN.pdf

HotelsParisEN.pdf

lundi 9 mai

09:00 → 12:30 Morning chair: Organizer

09:00 Registration & Welcome coffee

10:00 Adventures in Theoretical Physics (T: 50mn + Q: 10mn)

I give a qualitative description of a few problems in theoretical physics that I’ve thought about in recent years (the variety of ideas and techniques has a good overlap with some of Mike’s past interests). Topics will include a quantum field theory approach to determining Ricci flat metrics on K3 surfaces, D-brane models of theories of fractons, and a preliminary foray into theoretical biology.

Orateur: Prof. Shamit KACHRU (Stanford University)

Vidéo

11:00 Coffee break

11:30 Bootstrap for Lattice Yang-Mills Theory (T: 50mn + Q: 10mn)

I will speak about my recent work with Zechuan Zheng where we study the SU(Nc) lattice Yang-Mills theory in the ’t Hooft limit Nc → infinity, at dimensions D=2,3,4, via the numerical bootstrap method. It combines the Makeenko-Migdal loop equations, with the cut-off L on maximal length of Wilson loops, and the positivity conditions on certain correlation matrices. We thus obtain rigorous upper and lower bounds on the plaquette average at various couplings. The results are quickly improving with the increase of the cutoff L. In particular, for D=4 and L=16, the upper bound data in the most interesting weak-coupling phase are not far from the Monte-Carlo results and they reproduce well the 3-loop perturbation theory. We also attempt to extract the information about the gluon condensate from this data. Our results suggest that bootstrap can provide a tangible alternative to, so far uncontested, the Monte Carlo approach. I will also mention our bootstrap results for an "unsolvable" two-matrix model in the large N limit, where this method appears to be superior in efficiency over Monte Carlo.

Orateur: Prof. Volodya KAZAKOV (LPENS)

Vidéo

12:30 → 14:00 Lunch break

14:00 → 17:30 Afternoon chair: Laurent Baulieu

14:00 Exotic Fields, Tensionless Strings and Gravity (T: 50mn + Q: 10mn)

Orateur: Prof. Chris HULL (Imperial College)

Vidéo

15:00 Prolate Wave Operator and Zeta (T: 50mn + Q: 10mn)

This is joint work with Henri Moscovici in which we show that the ultraviolet spectrum of the selfadjoint extension of the prolate wave operator matches the squares of the zeros of the Riemann zeta function.

Orateur: Prof. Alain CONNES (IHES & Collège de France)

Vidéo

16:00 Coffee break

16:30 Remote Talk - Exotic Field Theories: Lifshitz Theory, Tensor Gauge Theory, and Fractons (T: 50mn + Q: 10mn)

Over the past few years, many exotic lattice systems with peculiar properties were found. Some of their peculiarities include particles with restricted mobility, large ground-state degeneracy, and long-distance sensitivity to short-distance details. Consequently, these theories do not have a standard continuum limit.

Together with Pranay Gorantla, Ho Tat Lam, and Shu-Heng Shao, we have explored these theories in detail using a field theory perspective.

In this talk, we will discuss the simplest examples of these theories, which are in one spatial dimension. These theories are not as rich and as robust as their higher-dimensional relatives. But they exhibit many of the subtleties in a simpler setting.

Orateur: Prof. Nathan SEIBERG (IAS)

Vidéo

mardi 10 mai

09:00 → 12:30 Morning chair: Curtis Callan

09:00 Quantum Complexity, Dynamical Chaos, and the Interior Structure of Black Holes (T: 50mn + Q: 10mn)

Orateur: Prof. Vijay BALASUBRAMANIAN (University of Pennsylvania)

Vidéo

10:00 Infrared Dynamics of QCD Theories (T: 50mn + Q: 10mn)

A new understanding of the infrared dynamics of QCD theories has emerged in recent years, leading to nonperturbative renormalization group flows of QCD theories. We will discuss some of these developments, including QCD theories that develop a mass gap, the endpoint of renormalization group flows, and the (conjectural) emergence of nonperturbative condensates.

Orateur: Prof. Jaume GOMIS (Perimeter Institute)

Vidéo

11:00 Coffee break

11:30 New Life of D-branes in Math (T: 50mn + Q: 10mn)

One of the most wonderful gifts from string theory to pure mathematics comes from Mike Douglas' ideas on the decay of D-branes and walls of marginal stability. Tom Bridgeland formalized structures discovered by Mike as stability conditions in abstract triangulated categories. This notion became central in modern homological algebra and is also pivotal in the theory of Donaldson-Thomas invariants.
I'll review several (hypothetical) extensions of the original picture, involving Fukaya categories with coefficients, non-archimedean B-model, etc.

Orateur: Prof. Maxim KONTSEVICH (IHES)

Vidéo

12:30 → 14:00 Lunch break

14:00 → 17:30 Afternoon chair: Adel Bilal

14:00 Flat Space Holography (T: 50mn + Q: 10mn)

Ever since the discovery of AdS/CFT duality 25 years ago, theorists have sought Minkowski space analogs. I will give an elementary introduction to some of the progress in recent years. First, I will say a bit about Mike.

Orateur: Prof. John SCHWARZ (Caltech)

Vidéo

15:00 Remote talk - Critical Points of Random Super-potentials and Spin Glasses (T: 50mn + Q: 10mn)

In the early 2000s, one often heard that the vacuum counting problem in string theory was like a spin glass problem. My talk will review results of Douglas, Shiffman, and myself on probabilistic methods for counting vacua of certain string theories. I then review some more recent results by various mathematicians on critical points of p-spin Hamiltonians. These results do not seem to be well known to physicists but may have analogs for string theory vacua.

Orateur: Prof. Steve ZELDITCH (Northwestern University)

Vidéo

16:00 Coffee break

16:30 Remote talk - BI for AI: Energy Conserving Dynamics for Optimization and Sampling (T: 50mn + Q: 10mn)

We introduce a novel framework for optimization based on energy-conserving Hamiltonian dynamics in a strongly mixing (chaotic) regime and establish some of its key properties analytically and numerically. The prototype is a discretization of Born-Infeld dynamics, with a squared relativistic speed limit depending on the objective function. This class of frictionless, energy-conserving optimizers proceeds unobstructed until slowing naturally near vanishing loss (up to a self-tunable hyper-parameter shift), which dominates the phase space volume of the system. Building from studies of chaotic systems such as dynamical billiards, we formulate a specific algorithm with good performance on machine learning and PDE-solving tasks, including generalization (so far studied at small scale). In progress are experiments on applications to computational chemistry, sampling, and larger-scale ML, along with further theoretical study of its impact on representation/feature learning. An application of this ML-inspired method to numerical PDE solving for string compactifications blends three of Mike’s many far-reaching insights.

Orateur: Prof. Eva SILVERSTEIN (Stanford University)

Vidéo

mercredi 11 mai

09:00 → 12:30 Morning chair: TBC

09:00 Persistent Spontaneous Symmetry Breaking at High Temperatures (T: 50mn + Q: 10mn)

I will describe the results of a series of works in which we have found systems for which Spontaneous Symmetry Breaking(SSB) persists to very high temperatures. The systems involve Conformal Field Theories of scalars in fractional dimensions 3<d<3 and for Gauge Theories in d=4. The systems are studied in the limit of various large numbers of species. In the process, we have found non-supersymmetric conformal manifolds as well as cases of non-supersymmetric effective potentials with flat directions. The SSB results in the formation of a dilaton.

Orateur: Prof. Eliezer RABINOVICI (HUJI)

Vidéo

10:00 Scale Separation in String Theory (T: 50mn + Q: 10mn)

Extra spacetime dimensions give rise to KK fields, whose masses should be large and in particular much larger than the cosmological constant. While this can happen naturally in an effective low-energy theory, it is not the case for most known vacuum solutions of ten-or eleven-dimensional supergravity. We review efforts to find vacua that resolve this tension and recent general bounds on KK masses.

Orateur: Prof. Alessandro TOMASIELLO (Univ. Milano Bicocca)

Vidéo

11:00 Coffee break

11:30 Truncated Affine Rozansky-Witten Models as Extended TQFTs (T: 50mn + Q: 10mn)

Mathematicians formulate fully extended d-dimensional TQFTs in terms of functors between a higher category of bordism and suitable target categories. Furthermore, the cobordism hypothesis identifies the basic building blocks of such TQFTs. In this talk, I will discuss Rozansky Witten models with affine targets, also known as 3-dimensional topologically twisted N=4 theories of free hypermultiplets. I will show how in this simple example the cobordism hypothesis can be systematically applied to explicitly construct the (infinite-dimensional) state spaces of this theory. Furthermore, a commutative Frobenius algebra will be identified that describes the extended TQFT restricted to circles and bordism between them (Based on work with Nils Carqueville and Daniel Roggenkamp).

Orateur: Prof. Ilka BRUNNER (Univ. München)

Vidéo

12:30 → 14:00 Lunch break

14:00 → 17:30 Afternoon chair: Ivan Kostov

14:00 Remote talk - Random Regular Graphs and Critical Phenomena in the Forest (T: 50mn + Q: 10mn)

The partition functions of perturbed ensembles of random regular graphs (RRG) which discretize 2d surfaces and yield perturbed pure 2d quantum gravity will be discussed. The phase transitions for the RRG perturbed by the chemical potentials for short cycles will be demonstrated numerically. The new matrix model for the massive spinless fermions interacting with 2d quantum gravity is found and solved in planar approximation interpolating between c=0 and c=-2 cases. Some aspects of the localization and ergodicity of modes in this model will be clarified.

Orateur: Prof. Alexander GORSKY (IITP RAS, MIPT)

Vidéo

15:00 Remote Talk - Square Dancing from the Viewpoint of a Mathematical Physicist (T: 50mn + Q: 10mn)

I will explain what modern western square dancing is and describe some mathematical viewpoints on the subject. The mathematics is neither complex nor deep, but it is fun.

Orateur: Prof. Greg MOORE (Rutgers University)

Vidéo

16:00 Coffee break

16:30 Remote Talk - Mike and Matrices (T: 50mn + Q: 10mn)

Orateur: Prof. Steve SHENKER (Stanford University)

Vidéo

jeudi 12 mai

09:00 → 12:30 Morning chair: Organizer

Machine learning/Neuro day

09:00 Deep Learning for Formal Reasoning (T: 50mn + Q: 10mn)

Here I will discuss the frontier of research for formal reasoning via deep neural networks. I will highlight the most recent progress in the area, especially automated theorem proving and automated formalization of natural language text. Also, I will discuss the role of language models, contrastive training, retrieval augmented modeling, and reinforcement learning toward the long-term goal of creating a system that can formalize and verify theories starting from a large natural language corpus.

Orateur: Prof. Christian SZEGEDY (Google Research)

Vidéo

10:00 Some News from the Semantic AI Paradise (T: 50mn + Q: 10mn)

The talk will make a (doomed?) attempt to convince the physicists in the audience that machine-based logic and proof combined with machine-based learning is a creeping revolution in science threatening their job security. In principle, I would like to ground it in at least some examples and demos of today's feedback loops between reasoning, conjecturing, and learning systems for math. But since this is a birthday party, it may also devolve into unhinged philosophizing attempts to understand what is math, physics, science, computing, AI, and their joint future.

Orateur: Prof. Josef URBAN (CIIRC)

Vidéo

11:00 Coffee break

11:30 Why Explain Mathematics to Computers? (T: 50mn + Q: 10mn)

A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. In this talk, I'll describe what formalization looks like, what kind of things it teaches us, and how it could even turn out to be useful (in our usual sense of "useful"). This will not be a talk about the foundations of mathematics, and I won't assume any prior knowledge about formalization.

Orateur: Prof. Patrick MASSOT (LMO, Université Paris-Saclay)

Vidéo

12:30 → 14:00 Lunck break

14:00 → 19:15 Afternoon chair: Organizer

14:00 Embedding of Low-Dimensional Attractor Manifolds by Neural Networks (T: 50mn + Q: 10mn)

Recurrent neural networks (RNN) have long been studied to explain how fixed-point attractors may emerge from noisy, high-dimensional dynamics. Recently, computational neuroscientists have devoted sustained efforts to understand how RNN could embed attractor manifolds of finite dimension, in particular in the context of the representation of space by mammals. A natural issue is the existence of a trade-off between the quantity (number) and the quality (accuracy of encoding) of the stored manifolds. I will here study how to learn the N2 pairwise interactions in a RNN with N neurons to embed L manifolds of dimension D<<N. The capacity, i.e., the maximal ratio L/N, decreases as ~ [log(1/e)]^-D, where e is the error on the position encoded by the neural activity along each manifold. These results derived using a combination of analytical tools from statistical mechanics and random matrix theory show that RNN are flexible memory devices capable of storing a large number of manifolds at high spatial resolution.

Orateur: Prof. Rémi MONASSON (LPENS)

Vidéo

15:00 Remote talk - Dependent Type Theory from the Perspective of Mathematics, Physics, and Artificial Intelligence (T: 50mn + Q: 10mn)

Dependent type theory imposes a type system on Zemelo-Fraenkel set theory (ZFC). From a mathematics and physics perspective dependent type theory naturally generalizes the Bourbaki notion of structure and provides a universal notion of isomorphism and symmetry. This comes with a universal substitution theorem --- isomorphic objects are inter-substitutable in well-typed contexts (Hofmann and Streicher 1995). From an AI perspective, or automated reasoning perspective, dependent type theory underlies the LEAN interactive verifier which is currently the go-to system for formal verification of mathematics. This talk will review dependent type theory as a discipline on set theory (the set model of type theory) and discuss approaches to improving automated reasoning based on SMT (SAT Modulo a theory) technology. This results in a class of inference algorithms under the name SAT modulo type theory or SMTT. Speculations on the relationship between SMTT and deep learning will be discussed briefly.

Orateur: Prof. David MCALLESTER (TTIC)

Vidéo

16:00 Coffee break

16:30 Remote talk - Computational Principles Underlying the Temporal Organization of Behavior (T: 50mn + Q: 10mn)

Naturalistic animal behavior exhibits a striking amount of variability in the temporal domain along at least three independent axes: hierarchical, contextual, and stochastic. First, a vast hierarchy of timescales links movements into behavioral sequences and long-term activities, from milliseconds to minutes. Second, action timing can be modulated by changes in context, of either internal (neuromodulatory, state-dependent) or external origin. Third, self-initiated actions exhibit large residual variability across repetitions, with signatures of stochastic origin. What computational principles underlie such complex temporal features? We will present the foundation of a theory of temporal variability in behavior and neural activity, based on metastable attractors observed in sensory and motor cortical areas. We will highlight the essential role played by intrinsic noise and heterogeneities in controlling the features of temporal variability.

Orateur: Prof. Luca MAZZUCATO (University of Oregon)

Vidéo

17:30 Cocktail party

vendredi 13 mai

09:00 → 12:30 Morning chair: Frank Ferrari

09:00 Radiation from Matrix Models (T: 50mn + Q: 10mn)

I give an overview of work characterizing radiation in generic four-dimensional conformal field theories. I argue that for theories with conformal scalars, the radiated energy is not positive definite and the radiated power is not Lorentz invariant. I then determine the coupling dependence of radiation, for N=2 superconformal field theories in the planar limit. This involves a purely combinatorial solution of certain matrix models, in terms of tree graphs.

Orateur: Prof. Bartomeu FIOL (University of Barcelona)

Vidéo

10:00 Flux Vacua and the Cosmological Constant (T: 50mn + Q: 10mn)

We construct vacua of string theory in which all moduli are stabilized, and the magnitude of the cosmological constant is exponentially small. The vacua are supersymmetric AdS solutions in flux compactifications of type IIB string theory on orientifolds of Calabi-Yau hypersurfaces. The vacuum energy is small because we ensure the exact cancellation of all perturbative contributions, through an explicit choice of integer parameters determined by the topology and quantized fluxes. The nonperturbative contributions that remain are exponential in these integers. Finding cosmological constants of small magnitude in this landscape is exponentially easier than in Bousso-Polchinski landscapes, but extending our approach to positive cosmological constants in realistic universes is a difficult open problem. Mike's vision for approaching the landscape statistically, as well as his profound contributions to the technical side of flux vacua, laid the foundation for this work.

Orateur: Prof. Liam MCALLISTER (Cornell University)

Vidéo

11:00 Coffee break

11:30 TBC (T: 50mn + Q: 10mn)

Orateur: Prof. Frederik DENEF (Columbia University)

12:30 → 14:00 Lunch break

14:00 → 16:00 Afternoon chair: Paul Windey

14:00 Remote talk - Spectral Flow Construction of $N=2$ Superconformal Orbifolds (T: 50mn + Q: 10mn)

Ten-dimensional Superstring theory unifies the Standard Model and quantum gravity. To obtain a four-dimensional theory with Space-Time Supersymmetry (which is necessary for phenomenological reasons), as shown by Candelas, Horowitz, Strominger, Witten, we must compactify six of the ten dimensions on a so-called Calabi-Yau manifold. Another equivalent approach to do the same is the compactification of 6 dimensions into an $N=2$ Superconformal field theory with the central charge $c=9$, as was shown by D. Gepner. Each of these two equivalent approaches has its own merits. In particular, Gepner's approach makes it possible to use exactly solvable N=2 SCFT models and thus obtain an explicit solution of the considered model.
The subject of my talk is a new approach to the construction of Calabi-Yau orbifolds of Fermat type required for the compactification in Superstring theory. The idea of the approach is to use the connection of the CY orbifolds with a class of exactly solvable N=2 SCFT models for explicitly constructing a complete set of fields in these orbifold models using the Spectral flow twist (Schwimmer and Seiberg) and the requirement of the mutual locality of the fields.

Orateur: Prof. Alexander BELAVIN (Independant University of Moscow)

Vidéo

15:00 Remote talk - How Natural is the Standard Model in the String Landscape? (T: 50mn + Q: 10mn)

Mike's pioneering work in taking a statistical approach to string vacua has contributed to an ever-improving picture of the landscape of solutions of string theory. In this talk, we explore how such statistical ideas may be relevant in understanding how natural different realizations of the Standard Model of particle physics are in the geometric framework of F-theory, where the landscape can be understood in terms of the vast moduli space of elliptic Calabi-Yau fourfolds connected by geometric transitions.

Orateur: Prof. Washington TAYLOR (MIT)

Vidéo