Calendar

For information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/quantum-matter-seminar/

The Emergence Proposal claims that in Quantum Gravity the kinetic terms of the the fields in the IR emerge from integrating out (infinite) towers of particles up to the QG cutoff. After introducing this proposal in the context of the Swampland Program, I will explain why it is natural to identify this QG cutoff with the Species Scale, motivating it by direct computation in the presence of the relevant towers. Then, I will present evidence for this proposal by directly studying how it is realized in different string theory setups, where the kinetic terms of scalars, p-forms and even scalar potentials can be shown to emerge after integrating out such towers.

Given integers g, m, and n, the heavy/light moduli space Mbar_{g, m|n} is a compactification of the moduli space of smooth (m+n)-marked curves of genus g. These spaces are particular examples of Hassett’s moduli spaces of weighted stable curves. Their rational cohomology gives a rich family of representations of products of symmetric groups. I’ll discuss recent work on the structure of this family of representations, and how they relate to the S_n-representations determined by the cohomology of Deligne-Mumford compactifications. This talk is based on joint work with Stefano Serpente and Claudia Yun.

https://sites.google.com/view/harvardmitag

When a collection of electronic excitations are strongly coupled to a single mode cavity, mixed light-matter excitations called polaritons are created. The situation is especially interesting when the strength of the light-matter coupling Ω_R is such that the coupling energy becomes close to the one of the bare matter resonance ω₀. For this value of parameters, the system enters the so-called ultra-strong coupling regime, in which a number of very interesting physical effects were predicted caused by the counter-rotating and diamagnetic terms of the Hamiltonian.

In a microcavity, the strength of the electric field caused by the vacuum fluctuations, to which the strength of the light-matter coupling Ω_Ris proportional, scales inversely with the cavity volume. One very interesting feature of the circuit-based metamaterials is the fact that this volume can be scaled down to deep subwavelength values in all three dimension of space.¹ Using metamaterial coupled to two-dimensional electron gases under a strong applied magnetic field, we have now explored to which extend this volume can be scaled down and reached a regime where the stability of the polariton is limited by diffraction into a continuum of plasmon modes².

We have also used transport to probe the ultra-strong light-matter coupling³, and show now that the latter can induce a breakdown of the integer quantum Hall effect⁴. The phenomenon is explained in terms of cavity-assisted hopping, an anti-resonant process where an electron can scatter from one edge of the sample to the other by “borrowing” a photon from the cavity⁵. We are also evaluating a proposal suggesting that the value of the quantization voltage can be renormalized by the cavity⁶.

1. Scalari, G. et al. Ultrastrong Coupling of the Cyclotron Transition of a 2D Electron Gas to a THz Metamaterial. Science 335, 1323–1326 (2012).
2. Rajabali, S. et al. Polaritonic Nonlocality in Light Matter Interaction. Nat Photon 15, 690–695 (2021).
3. Paravicini-Bagliani, G. L. et al. Magneto-Transport Controlled by Landau Polariton States. Nat. Phys. 15, 186–190 (2019).
4. Appugliese, F. et al. Breakdown of topological protection by cavity vacuum fields in the integer quantum Hall effect. Science 375, 1030–1034 (2022).
5. Ciuti, C. Cavity-mediated electron hopping in disordered quantum Hall systems. Phys. Rev. B 104, 155307 (2021).
6. Rokaj, V., Penz, M., Sentef, M. A., Ruggenthaler, M. & Rubio, A. Polaritonic Hofstadter butterfly and cavity control of the quantized Hall conductance. Phys. Rev. B 105, 205424 (2022).

For more information on how to join, please see: https://cmsa.fas.harvard.edu/event_category/topological-quantum-matter-seminar/

In nature, symmetry governs regularities, while symmetry breaking brings texture. In artificial neural networks, symmetry has been a central design principle, but the role of symmetry breaking is not well understood. Here, we develop a Lagrangian formulation to study the geometry of learning dynamics in neural networks and reveal a key mechanism of explicit symmetry breaking behind the efficiency and stability of modern neural networks. Then, we generalize Noether’s theorem known in physics to describe a unique symmetry breaking mechanism in learning and derive the resulting motion of the Noether charge: Noether’s Learning Dynamics (NLD). Finally, we apply NLD to neural networks with normalization layers and discuss practical insights. Overall, through the lens of Lagrangian mechanics, we have established a theoretical foundation to discover geometric design principles for the learning dynamics of neural networks.

To a connected reductive group G over a local field F we define a compact topological group π_1~(G) and an extension G(F)_∞ of G(F) by π_1~(G). From any character x of π_1~(G) of order n we obtain an n-fold cover G(F)_x of the topological group G(F). We also define an L-group for G(F)_x, which is a usually non-split extension of the Galois group by the dual group of G, and deduce from the linear case a refined local Langlands correspondence between genuine representations of G(F)_x and L-parameters valued in this L-group.

This construction is motivated by Langlands functoriality. We show that a subgroup of the L-group of G of a certain kind naturally leads to a smaller quasi-split group H and a double cover of H(F). Genuine representations of this double cover are expected to be in functorial relationship with representations of G(F). We will present two concrete applications of this, one that gives a characterization of the local Langlands correspondence for supercuspidal L-parameters when p is sufficiently large, and one to the theory of endoscopy.

This seminar will be held in Science Center 530 at 4:00pm on Wednesday, November 16th.

Please see the seminar page for more details: https://www.math.harvard.edu/~ctm/sem

I will discuss joint work with Christin Bibby, Nir Gadish, and Claudia Yun.  The historical antecedents are in earlier work of Billera-Holmes-Vogtmann around 2000 and others, who study an interesting space of metric trees on n labelled taxa. This is a space that is shellable and whose top homology was calculated, as an S_n-representation, by Robinson-Whitehouse.  These spaces have a reinterpretation as moduli of tropical curves of genus 0.  Other historical antecedents of our work are in the study of configuration spaces of n points on a graph, whose topological invariants are quite interesting. For example, Ko-Park proved that failure of planarity of a graph can be detected by torsion in H_1 of its unordered configuration space.

The work I will then describe concerns a genus g>0 analogue of the space of phylogenetic trees: the moduli space of tropical curves of genus g. Roughly speaking, this space parametrizes n-marked graphs of first Betti number g.  These spaces are no longer shellable for g>1, and their homology groups, as S_n-representations, are quite mysterious.  I will explain how making precise connections to compactified configuration spaces on graphs made it possible for us to make calculations in Sage when g=2 in a range beyond what was previously accessible.  These in turn produced new calculations and conjectures concerning the rational cohomology of M_{2,n}. No tropical geometry prerequisites are assumed in this talk.

Quasi-normal modes are complex exponential frequencies appearing in long time expansions of solutions to linear wave equations on black hole backgrounds. They appear in particular during the ringdown phase of a black hole merger when the dynamics is expected to be driven by linear effects. In this talk I give an overview of various results in pure mathematics which relate asymptotic behavior of quasi-normal modes at high frequency to the geometry of the set of trapped null geodesics, such as the photon sphere in Schwarzschild(-de Sitter). These trapped geodesics have two kinds of behavior: the geodesic flow is hyperbolic in directions normal to the trapped set (a feature stable under perturbations) and it is completely integrable on the trapped set. It turns out that normal hyperbolicity gives information about the rate of decay of quasi-normal modes, while complete integrability gives rise to a quantization condition.

This seminar will be held in person and on Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event/general-relativity-2021-22/

My lab is developing biophysical methods to achieve multicolor and dynamic biological imaging at the molecular scale. Our approach to capturing the dynamics of cellular processes involves cryo-vitrifying samples after known time delays following stimulation using custom cryo- plunging and high-pressure freezing instruments. To achieve multicolor electron imaging, we are exploring the property of cathodoluminescence — optical emission induced by the electron beam. We are developing nanoprobes (“cathodophores”) that will be used as luminescent protein tags in electron microscopy. We are applying these new methods to study G-protein- coupled receptor signaling and to visualize the formation of biomolecular condensates.

This seminar will be held in person and on Zoom. For more information on how to join, please see: https://cmsa.fas.harvard.edu/event/active-matter-seminar

McMullen proved that a stable family of rational maps is either trivial or all its members are Lattès. His proof relies on Thurston’s theorem on postcritically finite maps, which uses Teichmüller theory. I will discuss a recent new proof of McMullen’s theorem due to Zhuchao Ji and Junyi Xie which instead uses Berkovich dynamics over the complex Levi-Civita field.

For more information, please see:  Algebraic Dynamics Seminar at Harvard

In string theory one finds that states become massless as one approaches boundaries in Calabi-Yau moduli spaces. In this talk we look in the opposite direction, that is, we search for points where the mass gap for these light states is maximized — the so-called desert. In explicit examples we identify these desert points, and find that they correspond to special points in the moduli space of the CY, such as orbifold points and rank two attractors.

Beyond the tight/overtwisted dichotomy, 3-dimensional contact topology would appear to be dominated by flexibility: a central result of Eliashberg and Mishachev says that the contactomorphism group of the standard contact 3-ball has the homotopy type of the diffeomorphism group. In contrast with this, I will discuss how monopole Floer homology imposes constraints on the behaviour of families of contact structures on 3-manifolds. Applications include detecting exotic contactomorphisms given by certain “Dehn twists” on embedded spheres.