In this talk, I will show how to construct a holographic effective theory for the leading-twist multi-particle operators for $O(2)$ CFT in $d=3$ and $d=4-epsilon$. For $d=4-epsilon$ Wilson-Fisher fixed point. We obtain the Hamiltonian of the theory and show that it correctly reproduces all the dimensions at order ${mathcal O}(epsilon^2)$ of the leading twist operators for all values of the charge $Q$ and spin $J$. For $d=3$ strongly coupled $O(2)$ CFT, we find excellent agreement with $Q=3,4$ bootstrap data and inversion formula.
 
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Running Seminar
 
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Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
I will discuss the high-energy, small-angle limit of two-body classical gravitational scattering, focusing on the tower of multi-H diagrams that govern the leading logarithmic behavior. First, I will show that the recently developed SCET forward-scattering framework for gravity is fully equivalent to the multi-Regge expansion of the classical amplitude, reproducing exactly the s-channel multi-H diagrams. I will then compute the single-H diagram at two loops and the double-H diagrams at four loops, matching onto the classical eikonal phase in the ultrarelativistic limit. Finally, using dispersion relations, we establish a novel link between the high-energy logarithmic terms in the real and imaginary parts of the eikonal phase at 5PM order.
 
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Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Laurent Schwartz — EDP et applications
 

Séminaire Amplitudes et Gravitation sur l’Yvette (IHES/IPhT)
Perturbative field theory calculations are essential for precision predictions in collider and gravitational-wave physics. One of the major bottlenecks in such calculations is integration-by-parts (IBP) reduction of the underlying Feynman integrals. In this talk, I will argue that IBP reduction can be simplified by exploiting the infrared singularity structure encoded in the Landau equations. More precisely, I will show that the IBP syzygy module decomposes as a sum over the Fitting ideals associated with the individual components of the Landau locus. This decomposition provides an efficient method for constructing syzygies and suggests universality of solutions among integral topologies sharing the same infrared structure.
 
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I will report on an ongoing project in collaboration with Yannick Guedes Bonthonneau and Tobias Weich. The goal of this work is to define a natural spectrum associated with Anosov representations, consisting of complex hypersurfaces in the complexified dual Cartan subalgebra. The leading hypersurface corresponds to a well-known object in the literature — the so-called critical hypersurface of the representation. To some extent, this spectrum generalizes a similar notion in the rank-one case, known as the set of Pollicott-Ruelle resonances (and the leading resonance), which is known to encode the exponential decay of correlations, among other properties. I will describe the main consequences of this spectral approach, namely the meromorphic extension (to the full complexified dual Cartan subalgebra) of dynamical zeta functions and Poincaré series associated with the representation. If time permits, I will discuss specific values of these functions, the sharp quantitative decay of correlations for the refraction flow, and the perspectives for future work.
 

I will present several results on the topology of closed manifolds of dimension at least 4 that admit a (real) properly convex projective structure, all related to a vanishing theorem of Kobayashi from 1984 for the rational Pontryagin classes. In arbitrary dimensions, I will outline a classification of locally symmetric manifolds admitting properly convex projective structures. Focusing on dimension 4, I will then present a result on the geometric decomposition which is the analogue of a theorem of Benoist in dimension 3, and the construction of examples that realize all possible positive values of the Euler characteristic. Based on joint work with Stefano Riolo and Leone Slavich.
 

Running Seminar
In abstract Hodge theory, Deligne’s delta splitting measures how far a mixed Hodge structure is from being split as a real mixed Hodge structure. An allied notion, developed by S. Bloch, R.Hain et al., is that of a height for a special class of mixed Hodge structures called Biextensions.
The idea of a Biextension is closely related to algebraic cycles homologous to zero. Given two such cycles in complementary codimensions in an ambient smooth and projective variety, a certain cohomology group associated to the pair provides an example of a Biextension-type mixed Hodge structure.  The height associated with such a Biextension has been well studied and has been an active area of research for the past few decades.
 In an ongoing project, the speaker, along with J. I. Burgos Gil and G. Pearlstein, has developed a theory of mixed Hodge structures and heights associated with Bloch’s higher cycles, that generalizes the above study of Biextensions (doi.org/10.1112/plms.12443 and arXiv:2410.17167v2 [math.AG]).
 In the talk, I will explain the current state of the art of this project after reviewing the established theory.
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In joint work in progress with Hevesi, Thorne and Whitmore, we prove that automorphic Galois representations over CM fields are de Rham and have the expected Hodge–Tate weights. The novelty of our result is that we do not impose any assumptions on the residual mod p Galois representation. To achieve this, we prove a theorem on the cohomology of certain unitary Shimura varieties, which gives a bound on the maximal order of a torsion class in the lower half of degrees of cohomology. After placing this theorem in the right context and discussing its proof, I will sketch how it relates to the de Rham property of automorphic Galois representations.
 
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Running Seminar
A survey of results on regulators in Calabi-Yau families will be given.
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