Seminars

The emergence of antibiotic resistance is a major clinical challenge of the present day. To understand and predict the phenomenon, one must be able to quantitatively describe the evolutionary paths leading to resistance acquisition. I will present our contribution to this problem in two parts. In the first part, I will introduce a model based on empirical dose-response curves in which a bacterial fitness landscape changes systematically with drug concentration. The model predicts that epistasis, i.e. the interaction between mutational effects, is maximized at intermediate drug concentration. Despite the high ruggedness of the landscapes, we find the unexpected property that all fitness peaks are accessible from the wild type regardless of the concentration. We further predict that resistance evolves in two distinct phases involving the interplay of two different phenotypes, the quantitative features of the phases being determined by the drug concentration. In the second part, I will discuss the repeatability of the fixation of resistance mutations, which is a first step towards understanding the predictability of antibiotic resistance evolution. I will show how a heavy-tailed distribution of the fitness effects of mutations makes the degree of repeatability a non-self-averaging random variable. By applying this to data on resistance to the drug cefotaxime, I will demonstrate that at high concentration of the drug, the repeatability of fixation depends on the identity of resistance mutations and cannot be determined from the distribution of fitness effects alone.

Quantum computing is currently one of the most active areas of research, mainly due to its ability to outperform classical computing for certain computational tasks. We will look at quantum computing through the lenses of two central and closely-related models of computation: query complexity and communication complexity. The majority of provable advantages of quantum computing over classical computing are found within these models, which makes them crucial. In this talk, I will discuss quantum query and communication complexity, with a focus on the role of symmetry. Along the way I will give a brief overview of some of my results and current research interests. I will describe the problem of quantum query-to-communication simulation. It is a well-known fact that classical query algorithms for an n-bit Boolean function can be simulated to give communication protocols of a related communication problem with only a constant overhead. Buhrman, Cleve and Wigderson (STOC'98) showed that this query-to-communication simulation can also be performed in the quantum world, however, with an O(log n) overhead. Whether this overhead is necessary was a long-standing open problem. We resolve this open problem, with symmetry associated with Boolean functions playing a central role. We will also explore how symmetry affects the relationship between complexity measures of Boolean functions and can be exploited in designing quantum algorithms for computing over noisy data. This talk is based on an ongoing work and the following papers: - Quantum Query-To-Communication Simulation Needs a Logarithmic Overhead. Sourav Chakraborty, Arkadev Chattopadhyay, Nikhil S. Mande and Manaswi Paraashar. QIP 2020 and CCC 2020. - Symmetry and Quantum Query-to-Communication Simulation. Sourav Chakraborty, Arkadev Chattopadhyay, Peter Hoyer, Nikhil S. Mande, Manaswi Paraashar and Ronald de Wolf. STACS 2022. - Separations Between Combinatorial Measures for Transitive Functions. Sourav Chakraborty, Chandrima Kayal and Manaswi Paraashar. ICALP 2022. - Randomized and quantum query complexities of finding a king in a tournament. Nikhil S. Mande, Manaswi Paraashar and Nitin Saurabh. FSTTCS 2023. - Local Correction of Linear Functions over the Boolean Cube. Prashanth Amireddy, Amik Raj Behera, Manaswi Paraashar, Srikanth Srinivasan and Madhu Sudan. STOC 2024. - On the communication complexity of finding a king. Nikhil Mande, Manaswi Paraashar, Swagato Sanyal and Nitin Saurabh. Manuscript. 2024.

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Thesis defence (hybrid): Join Zoom Meeting https://zoom.us/j/93280841386 Meeting ID: 932 8084 1386 Passcode: 039996 The Macdonald polynomials are a remarkable family of symmetric functions which generalises many known family of symmetric functions, such as the Schur functions and the monomial symmetric functions. In the first part of the talk we will describe a conjecture of J. Haglund which says roughly that the normalized integral form Macdonald polynomials are Schur positive. We will discuss some partial results towards this conjecture. In the second part of the talk we will describe the product rules for type SL2 Macdonald polynomials P_m P_l and E_m P_l where P_m and E_m are the symmetric and nonsymmetric Macdonald polynomials respectively. We will discuss some techniques from double affine Hecke algebra which helps us compute the product rules. This part is a joint work with Arun Ram

Embryos often communicate instructions to their cells using diffusible signaling molecules called morphogens. In textbook models, morphogens diffuse from a localized source to form a concentration gradient, and target cells select fates by measuring the local morphogen concentration. However, natural patterning systems often incorporate numerous co-factors and extensive signaling feedback, suggesting that embryos require additional means of control to generate reliable patterns. This talk will present our recent results that illuminate how additional regulatory features enable robust pattern formation by the morphogen Nodal in zebrafish embryogenesis. Using a series of mutant embryos engineered to have feedback-compromised patterning systems, we demonstrate that simple ligand diffusion and capture is sufficient to explain the formation of normal Nodal signaling patterns. We further demonstrate that embryos regulate pattern features by tuning ligand capture with cell surface receptor complexes. Finally, we show that negative feedback on signaling, though dispensable under normal circumstances, is required to correct perturbations. Collectively, these results establish the Nodal patterning system as an exciting model for robust developmental patterning. Join Zoom Meeting https://zoom.us/j/91019034916 Meeting ID: 910 1903 4916 Passcode: 994404

2 - week Workshop on Mathematical Modeling in Development Biology

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)

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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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