Seminars

Thesis defence (hybrid): ------------------------- Join Zoom Meeting https://zoom.us/j/99549679295 Meeting ID: 995 4967 9295 Passcode: 323624 -------------------------------------------------------------- In this talk, we will describe two independent results based on my thesis. The first is on a unique factorization property for tensor products of parabolic Verma modules. More precisely, we give a necessary and sufficient condition for when products of characters of two collections of parabolic Verma modules (and their restrictions to some subalgebras of the Cartan subalgebra) are equal. The second part is on the factorization phenomenon of flagged skew Schur polynomials upon twisting the variables by roots of unity. These flagged skew Schur polynomials include an interesting family of Demazure characters as a special case. -------------------------------------------------------------------

2 - week Workshop on Mathematical Modeling in Development Biology

In [Radchenko & Villegas, Bull. Lond. Math. Soc., 2021], Radchenko and Villegas proved that a finite simple graph G is chordal if and only if the inverse of the independence polynomial of G is Horn hypergeometric. In this talk, we present a new proof of their result using some elementary combinatorial methods and also generalize their result to POE graphs that could possibly have a countably infinite number of vertices. Our proof is based on the connection between the independence polynomial of G with the multi-colored chromatic polynomials of G which was established first in [Arunkumar, Kus, and Venkatesh, J. Algebra, 2018].

This talk, split into two parts, will be on how symmetry principles can help us identify new phases of matter. In the first part (based on [1,2]), I will introduce a novel system of classical 'fractons' which exhibit a remarkable set of features defying conventional expectations from almost all known classical mechanical systems. This includes the disassociation of velocity and momenta, the appearance of attractors seemingly in violation of Liouville's theorem, the formation of crystalline structures, evading the famous theorem by Hohenberg, Mermin, Wagner and Coleman and the failure of statistical mechanics. I will show that all this is a robust feature of underlying symmetries which enforces 'Machian' dynamics wherein isolated particles are immobile, and motion requires the assistance of proximate particles. In the second part of my talk (based on [3,4]), I will discuss how new gapless phases emerge when unbroken microscopic symmetries manifest themselves in distinct ways on infrared fields. I will demonstrate the existence of several `symmetry-enriched' critical phases in the phase diagram of well-known coupled spin ladders which have been missed in all previous study. One of these is also a gapless topological phase and hosts protected edge modes of a distinct nature compared to their gapped counterparts. [1] Phys. Rev. B 109, 054313 (2024) [2] arXiv:2312.02271 [3] Phys. Rev. Lett. 130, 256401 (2023) [4] Phys. Rev. B 108, 245135 (2023)

See https://sites.google.com/view/seminar-prismatic-cohomology/home

2 - week Workshop on Mathematical Modeling in Development Biology

Spontaneous symmetry breaking underpins some of the most important phenomena in condensed matter and statistical physics. A description of direct transitions between symmetry breaking phases in terms of local order parameters is formulated when the symmetry breaking patterns were Landau-compatible i.e. when the unbroken symmetries of one phase is a subset of the other. About twenty years ago, Senthil et al [1] demonstrated that a direct transition between Landau-incompatible symmetry breaking phases was also possible in two-dimensional quantum magnets. Such 'deconfined quantum critical' (DQC) transitions are believed to be exotic and found in interacting quantum systems, often with anomalous symmetries (e.g.: constrained by Lieb-Schultz-Mattis theorems). In this talk (based on upcoming work with N. Jones), I will demonstrate that such special conditions are unnecessary and Landau-incompatible transitions can be found in a well-known family of classical statistical mechanical models introduced by Jose, Kadanoff, Kirkpatrick and Nelson [2]. All smoking-gun DQC features such as charged defect melting and enhanced symmetries are readily understood. I will also show that a closely related family of models also exhibits another unusual critical phenomenon found in quantum systems- 'unnecessary criticality' where a stable critical surface exists within a single phase of matter analogous to the first-order line separating liquid and gases. [1] SCIENCE, Vol 303, Issue 5663 [2] Phys. Rev. B 16, 1217 (1977)

2 - week Workshop on Mathematical Modeling in Development Biology

TBA

2 - week Workshop on Mathematical Modeling in Development Biology

Many interesting phenomena are going to be tested in the upcoming Electron-Ion Collider. One of them could be the Bose enhancement of gluons in the nuclear wave function. Bose enhancement leads to an enhancement of diffractive dijet production cross section when the transverse momenta of the two jets are aligned at zero relative angle. This enhancement is maximal when the magnitude of the transverse momenta of the two jets are equal, and disappears rather quickly as a function of the ratio of the two momenta. This can be shown for both the dilute limit and fully nonlinear dense regime where the nuclear wave function is evolved with the leading order JIMWLK equation. In both cases we observe a visible effect, with it being enhanced by the evolution due to the dynamical generation of the color neutralization scale.

2 - week Workshop on Mathematical Modeling in Development Biology

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2 - week Workshop on Mathematical Modeling in Development Biology

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2 - week Workshop on Mathematical Modeling in Development Biology

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2 - week Workshop on Mathematical Modeling in Development Biology

Actin is an essential protein required for force generation in key cellular processes including cytokinesis, cell migration, phagocytosis etc. Intracellular actin networks are thought to assemble by polymerization of filaments at their barbed ends and depolymerization at their pointed ends. This process, referred to as “treadmilling”, forms the central bedrock of our current understanding of actin dynamics. However, recent results from our lab suggest that this “dogma” might not be true. By using a combination of multicolor single-molecule and single filament experiments as well as mathematical modeling, we uncovered two distinct mechanisms which facilitate barbed end depolymerization and pointed ends polymerization; overturning the treadmilling “dogma”. Twinfilin, Cofilin, and Profilin, three key actin binding proteins have been shown to individually depolymerize barbed ends, however, how they collectively regulate barbed end depolymerization remains an open question. Therefore, we decided to investigate the multicomponent dynamics of twinfilin, cofilin, and profilin at the barbed end. We have discovered that twinfilin competes with profilin and promotes binding of cofilin to the sides. Interestingly, contrary to previous expectations, we found that profilin and cofilin can simultaneously bind the same barbed end resulting in its accelerated depolymerization. Additionally, we discovered the first ever pointed end polymerase VopF, which processively tracks pointed ends for several minutes and in the process accelerates their elongation. Using single-molecule force-spectroscopy, we found that VopF is mechanosensitive - its rate of polymerization increases under pN-range pulling forces. Taken together, our new findings challenge the basic tenets of our current understanding of intracellular actin dynamics and call for taking a fresh look.

See https://sites.google.com/view/seminar-prismatic-cohomology/home

2 - week Workshop on Mathematical Modeling in Development Biology

2 - week Workshop on Mathematical Modeling in Development Biology

2 - week Workshop on Mathematical Modeling in Development Biology

In this talk, I will present our work on relating atomic-level protein dynamics to its functions, e.g., biological signaling. Cells and organisms react to external and internal signals by proteins that consist of sensor and effector modules. Sensors detect environmental changes, such as light, pH, hormones, etc., while corresponding effectors trigger a response. First, I will discuss the initial step for signaling, i.e., drug molecules binding to proteins. I will exemplify this with our recent simulation and theoretical modeling efforts in collaboration with experimentalists to understand polyelectrolyte–protein interactions and help design polymers for SARS-CoV-2 virus inhibition. Later, I will introduce basic statistical-mechanics concepts to derive transmit functions that describe how a local time-dependent perturbation, which can be a deformation or a force, propagates in a viscoelastic medium such as a protein. Transmit functions are defined by equilibrium fluctuations fromsimulations or experimental observations. We apply this framework to our molecular dynamics simulation data of a bacterial signaling protein, for quantifying signal transfer efficiency of its principal deformation modes, namely shift, splay, and twist. Finally, I will conclude the talk with a few future research directions.

The conventional approach to LHC analysis involves comparing the measured data to Monte Carlo simulations. These simulations start at the hard-scattering level, where the potential for new physics is maximal, and proceed through various stages, including showering, hadronization, and detector response. Unfortunately, each stage introduces complexities, resulting in a convoluted representation of the true underlying physics at the simulated detector level. Events measured at the LHC detector are also a somewhat convoluted version of the true underlying physics, due to various latent effects. Eliminating these convolutions is essential for a direct comparison between theoretical predictions and measured data, which can be achieved through the process of 'Unfolding', where reconstructed or measured events are directly mapped to the hard-scattering level. In this seminar, I will discuss the development and application of multi-dimensional unfolding models that utilize machine-learning-based generative techniques, specifically Generative Adversarial Networks and Normalizing Flows. A key focus will be on how multi-dimensional unfolding with NFs allows the reconstruction of observables in their proper rest frame and in a probabilistically faithful way. I will highlight its practical impact through a case study on the measurement of CP-phase in the top Yukawa coupling.