Speaker:   Bradley Dirks

Abstract:  
Griffiths showed that, for smooth hypersurfaces, Hodge theory can be described using rational forms with controlled pole order. For singular hypersurfaces, Hodge ideals measure the difference between pole order and the Hodge filtration.

I will discuss a higher-codimensional analogue for local cohomology. If X is a closed subvariety of a smooth variety Y, the local cohomology modules carry a Hodge filtration due to Saito. By construction, they also carry a natural filtration coming from infinitesimal neighborhoods of X in Y. I will explain why the Hodge filtration is contained in this infinitesimal filtration, and discuss consequences for injectivity theorems. Joint with Qianyu Chen and Sebastián Olano.

Speaker:   Vlad Rosenhaus
Title:   Field theory of wave turbulence - part 2

Speaker:   Carlomassimo Casciola

Title:   Polymer flows

Speaker:   Nils Hemmingsson

Abstract:  
A holomorphic correspondence on C is a multivalued map defined by a polynomial in two variables. I will discuss work in progress on the dynamics of such maps. In particular, I will present a formula for the Lyapunov exponent of the family w^2=z^3+c with respect to the equilibrium measure. Based on joint work with Vanessa Matus de la Parra, Sabya Mukherjee and Misha Lyubich.

Speaker:   Michal Shavit

Title:   This is my talk

Abstract:   this is my abstract

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Speaker:    Anuj Kumar 
Title:   
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Speaker:   Sergey Nersisyan

Abstract:  
TBA

Speaker:     Dina Soltani Tehrani

Title:  
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Speaker:      Michele Dolce 
Title:   Instability of the 2D Taylor-Green vortex
Abstract:   The 2D Taylor-Green (TG) vortex (aka cellular flow) is the prototypical example of an Euler steady state on T^2 possessing truly two-dimensional features, like elliptic and hyperbolic stagnation points. Its streamfunction, sin(x)sin(y), lives on the second Fourier shell, making it susceptible to large-scale destabilizing mechanisms. Despite the apparent simplicity of the steady state, a proof of its spectral instability has long remained elusive, and was only recently observed numerically. To solve this problem, I will introduce a new criterion to detect unstable eigenvalues for a wide class of linear Hamiltonian operators. We apply this to prove the stability of the TG vortex with respect to odd perturbations. In the subspace of functions even in both variables, we combine our criterion with a rigorous computer-assisted argument to locate two unstable eigenvalues. This fully characterizes the unstable spectrum of the TG vortex and implies nonlinear instability in velocity. This is a joint work with G. Cao-Labora, M. Colombo and P. Ventura.
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Speaker:   Tommaso Rosati  
Title:   Lyapunov exponents for linear cocycles driven by stochastic Navier-Stokes
Abstract:   We provide the first convergence result for finite time Lyapunov exponents of Passive Scalar Advection and Linearized Stochastic Navier-Stokes (two linear cocycles driven by the stochastic Navier-Stokes equations). The proof is based on establishing unique ergodicity for a Markov process with values in an infinite-dimensional projective space. Uniqueness of the invariant measures requires an extension of asymptotic coupling tools, and proving a generic non-collinearity for passive scalar advection. Joint work with Sam Punshon-Smith.
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Speaker:    Patrick Diamond

Title:   Nonlinear processes regulating zonal flow amplitude in collisionless drift-Rossby turbulence

Abstract:  

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Speaker:   Gautam Iyer

Title:   
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Speaker:    Kyle Liss

Title:   
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Speaker:    Camilla Nobili

Title:   From Boundary Layers to Ultimate Scaling: Covariance Design and Transport Bounds in Thermal Convection
Abstract:  A central question in turbulent thermal convection is how near-wall bound- ary layers and bulk turbulent fluctuations constrain the global heat transport (Nu). In this talk, we explore the scaling bounds of thermal transport using a stochastic framework that bridges kinematic limits with dynamical parameteri- sations.The presentation is divided into two parts. In the first part, we consider a generic, incompressible stochastic velocity field with a given energy budget. In the spirit of wall-to-wall optimal transport (e.g., Hassanzadeh, Chini & Doering, 2014), we show that near-wall geometric decay universally caps transport at an asymptotic limit of Nu ≲ Pe2/3 as Pe → ∞. In the second part, coupling the thermal field to Stokes dynamics, we investigate how specific covariance struc- tures of temperature fluctuations select between classical turbulent regimes. By tuning the spatial covariance matrix, we systematically reconstruct both the Malkus Ra1/3 scaling and the Kraichnan–Spiegel Ra1/2 ”ultimate” regime. This approach provides a direct geometric and statistical mechanism explaining how turbulent correlation lengths in the bulk versus the boundary layer dictate macroscale heat transfer.
This work is joint with Franco Flandoli and Theresa Lange.

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Speaker:     Alexandros Alexakis

Title:   

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Speaker:      Renzo Ricca

Title:   

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Speaker:   Victor Steinberg

Title:   

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Speaker:    Anna Frishman

Title:   

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Speaker:     Timo Schorlepp

Title:   

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Speaker:   Eric Jovinelly

Abstract:  
Rational curves are intricately linked to the birational geometry of varieties containing them. Certain curves, called free curves, have the nicest deformation properties. However, it is unknown whether mildly singular Fano varieties contain free rational curves in their smooth locus. In this talk, we discuss free curves of higher genus. Using recent results about tangent bundles, we prove that any klt Fano variety has higher genus free curves. We then use the existence of such free curves to get some applications: we prove the existence of free rational curves in terminal Fano threefolds; study the fundamental group of the smooth locus of a Fano variety; and obtain a new characterization of projective space via lengths of extremal rays. This is joint work with Brian Lehmann, Eric Riedl, and Osamu Fujino.

Speaker:     Greg Eyink

Title:   

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Speaker:     Guido Boffetta

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Speaker:      Nir Navon

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Speaker:   Gilbert Weinstein

Speaker:    Alexei Maliybaev

Title:   Perturbative anomalous exponents from Kolmogorov multipliers

Abstract:  Intermittency, manifested through anomalous scaling, remains one of the central unresolved problems in turbulence theory, with few analytical approaches extending beyond idealized linear transport models. We introduce a perturbative framework for anomalous scaling in turbulent transport based on multiplier statistics, rather than zero-mode calculations. We demonstrate the approach using a shell model combining deterministic and Kraichnan-like stochastic components. We reduce the problem to the analysis of a stationary Fokker-Planck equation for Kolmogorov multipliers, defined as ratios of successive scalar amplitudes. Its solution yields the invariant measure through a perturbative expansion around a Gaussian distribution. Using the resulting multiplier statistics, we compute explicit anomalous scaling exponents for structure functions of arbitrary order, including odd, even, and non-integer moments. Although demonstrated here for a shell model, the framework suggests a systematic perturbative route toward analytical theories of intermittency in turbulence. This is a joint work with Simon Thalabard.

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Speaker:   Nigel Goldenfeld

Title:   

Abstract:  

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