The Institute of Mathematical Sciences (IMSc), founded by Alladi Ramakrishnan in 1962, is a national institution for research in frontier areas of computational biology, computer sciences, mathematics and theoretical physics. The institute members are also actively engaged in training young researchers through a vibrant doctoral program and also sharing the wonders of theoretical and computational sciences to school and college students. This year we are celebrating the 60th foundation year of our institute by honouring young and experienced scientists who have made fundamental contributions in their areas of research, through the IMSc Diamond Jubilee Colloquium Series.

### Topology at High Temperature from the Lattice

#### Prof. Dr. Guy Moore

QCD fields can possess nontrivial topology - instantons. The density of instantons is strongly temperature dependent, and this temperature dependence is important to the early-Universe dynamics of the hypothetical axion particle, which may form the dark matter of the Universe. A secure lattice measurement of topological susceptibility up to about 1.1 GeV temperatures would allow a precision prediction of the axion mass. I explain the obstacles to such a determination, and I introduce a novel set of computational techniques which can help to overcome them.

##### Venue: Online and screened live at Ramanujan Auditorium

PASSCODE FOR ZOOM MEETING: 200887

### Observing a changing Hilbert-space inner product

#### Prof. Barry Sanders

##### Director, Institute for Quantum Science and Technology, Department of Physics and Astronomy, University of Calgary, Canada

In quantum mechanics, physical states are represented by rays in Hilbert space H, which is a vector space imbued by an inner product, whose physical meaning arises as the overlap $\braket{\phi|\psi}$ for $\ket{\psi}$ a pure state (description of preparation) and $\bra{\phi}$ a projective measurement. However, current quantum theory does not formally address the consequences of a changing inner product during the interval between preparation and measurement. We establish a theoretical framework for such a changing inner product, which we show is consistent with standard quantum mechanics. Furthermore, we show that this change is described by a quantum operation, which is tomographically observable, and we elucidate how our result is strongly related to the exploding topic of PT-symmetric quantum mechanics. We explain how to realize experimentally a changing inner product for a qubit in terms of a qutrit protocol with a unitary channel.

##### Venue: Online

PASSCODE FOR ZOOM MEETING: 200887

### Fast Neutrino Oscillations: Beginning and End

#### Prof. Basudeb Dasgupta

##### Tata Institute of Fundamental Research, Mumbai

I will discuss fast flavor oscillations - a novel kind of neutrino oscillation that becomes possible if the neutrino density is large, as may happen inside supernovae, in neutron star mergers, and in the early universe. I will first discuss a condition that must be fulfilled for such oscillations to start. Then I will discuss what is the possible end result of these rapid flavor oscillations occurring over less than a centimetre, including their possible impact on stars and element creation.

##### Venue: Ramanujan Auditorium




### Decoding the Path Integral: Resurgence and Nonperturbative Physics

#### Prof. Gerald Dunne

##### University of Connecticut

How do quantum systems behave under extreme conditions such as ultra-high density and ultra-high intensity? This question has applications in a wide range of physical contexts, from condensed matter to particle and nuclear physics, and to astrophysics. The answer requires going beyond perturbation theory, directly to the path integral representation of quantum field theory. However, there are several important conceptual and computational problems concerning quantum path integrals under extreme conditions, which have recently been approached from new perspectives motivated by resurgent asymptotics, a novel mathematical formalism that effectively unites perturbative and non-perturbative physics. This talk will review the basic ideas behind the connections between resurgent asymptotics and physics, starting from the work of Airy and Stokes on rainbows, and the development of trans-series by Ecalle, and then turn to some recent applications in quantum mechanics and quantum field theory.

### The QCD critical point

#### Prof. Thomas Schaefer

##### North Carolina State University

I summarize arguments that suggest that the phase diagram of QCD, the theory of quarks and gluons, has a critical endpoint which is analogous to the endpoint of the water-vapor transition. This point marks the onset of a first order phase transition between a quark-gluon vapor and a hadronic liquid. I will argue that the critical point can be searched for in collisions of relativistic heavy ions. The main observables are fluctuation measurements, and the expected signatures are related to critical opalescence. I summarize the ongoing theoretical and experimental efforts devoted to observing signatures of critical fluctuations. I argue that along the way, we have gained new insights into an old theory, fluid dynamics.

### Machine learning for lattice field theory and back

#### Prof. Gert Aarts

##### Director, ECT* Trento and Department of Physics, Swansea University

Recently, machine learning has become a popular tool to use in fundamental science, including lattice field theory. Here I will report on recent progress, starting with (by now) basic applications (phase transitions and critical exponents), moving on to new ideas for the Inverse Renormalisation Group and ending with more speculative suggestions on quantum-field theoretical machine learning.

### Quantum channels and black holes

##### Indian Institute of Technology Madras

Black hole information paradoxes are at the heart of the mysteries of quantum spacetime. Black hole interiors pose the most profound challenges of our understanding of the holographic principle which states that quantum spacetime can be encoded into degrees of freedom of an ordinary quantum system living at the boundary. Recently quantum information theory together with some simple tractable models has played a major role in elucidating how the long standing information paradoxes of black holes can be resolved, and how the black hole interiors can be decoded from the Hawking radiation via appropriate quantum channels. Other developments have pointed out that black hole dynamics can teach us the basic principles of quantum thermodynamics necessary to realize constructions of fault tolerant quantum memory and quantum gates, and efficient ways for constructing other quantum channels such as teleportation channels using strongly interacting systems, I will review some aspects of these developments, and briefly some reasons to believe why black hole microstates can also give us the key to understanding some phases of matter like strange metals.

### Athermal Elasticity: From Crystalline to Amorphous Packings

#### Kabir Ramola

##### Tata Institute of Fundamental Research, Hyderabad

Elasticity is a fundamental macroscopic property that emerges in any collection of interacting particles. However, at sufficiently low temperatures where thermal fluctuations are negligible, a free energetic description of such macroscopic properties is not available. Granular materials and glasses offer a paradigm where disorder in the arrangements of particles plays a fundamental role in determining the energy landscape, and thereby their stability, response and elasticity properties. Gradually introducing disorder into athermal crystalline packings can be used to build a relation between the well-established physics of crystals and that of amorphous solids. Such studies can also reveal interesting phenomena peculiar to athermal systems such as hidden order-disorder transitions. In this talk I will outline the development of exact theoretical techniques which can be used to characterize fluctuations in positions, forces and interaction energies in near-crystalline athermal systems, which offer a route towards understanding the emergent elasticity properties of ubiquitous amorphous solids.

### A Golden Age in High Energy Nuclear Physics

#### Prof. Rob Pisarski

##### Brookhaven National laboratory

I briefly review the modern theory of strong interactions, Quantum ChromoDynamics, and why we believe that a qualitatively new state of matter, a Quark-Gluon Plasma, is created in the collisions of heavy ions at very high energies. I discuss, in particular, why it may be the most "ideal" liquid on earth, and the phenomenon of jet quenching. I conclude by discussing what happens when one goes down in energy, and how that may probe qualitatively new states, including a Critical End-Point and Quantum Pion Liquids.

### Supercomputing the properties of strong interaction matter

#### Prof. Dr. Frithjof Karsch

##### Bielefeld University

Strongly interacting matter at temperatures more than 100.000 times larger than in the interior of our sun and at an order of magnitude larger densities than in atomic nuclei existed in the early universe and is studied today experimentally on earth in ultra-relativistic collisions of heavy-ions. The exploration of properties of such hot and dense matter also is subject to intensive theoretical research. Computer simulations of the theory of strong interactions, Quantum Chromodynamics (QCD), performed on discrete space-time lattices provide a powerful framework for the study of such matter. These simulations provide insights into the phase structure of strong interaction matter described by QCD and allow first principle calculations that can be confronted with experimental results obtained in heavy-ion collisions. We give a brief overview of the development of lattice QCD calculations at finite temperature and density and discuss computational requirements for state-of-the-art numerical calculations. We furthermore present results from studies of the chiral phase transition in QCD as well as a new, high statistics determination of the QCD equation of state. Some results on fluctuations of conserved charges and their higher order cumulants will be discussed and compared with experimental results.

### Dispersion Relations: From Classical Optics to String Theory

#### Prof. N. D. Hari Dass

##### Retd. Senior Professor, The Institute of Mathematical Sciences

I shall give a pedagogical narration of how a simple, but intriguing relation about colors in classical optics impacted the most modern developments in physics, even to the point of anticipating String Theory. The strong thread that held these pearls of scientific creativity was the powerful mathematical idea of analyticity, which in this physical context turned out, rather surprisingly, to be a consequence of the deeply cherished physical principle of causality. The talk will be at a level accessible to a wide audience.

### Emergent electromagnetism in Jammed granular solids

#### Prof. Subhro Bhattacharjee

##### ICTS-TIFR Bengaluru

Emergence of low energy degrees of freedom is a recurrent theme in condensed matter systems. In more familiar systems such as crystalline solids the emergence of phonons as collective modes of vibration are associated mainly with broken translational symmetry that governs the physics at low temperatures. However, in a wide class of systems, local energetic constraints may take the form of Gauss's law giving rise to an emergent electromagnetism at low energies. In this talk, I shall start with a brief review of such emergent electromagnetism in discussing their basic features as well as the general settings in which they appear. Then I shall apply it to understand the mechanical response of naturally abundant granular solids such as sand grains where local conditions of mechanical equilibrium, i.e., force and torque balance on each grain, as I shall show, have the mathematical structure of a generalized Gauss's law for a rank-2 U(1) electromagnetism. The electrostatic limit of this tensor electromagnetism successfully captures the anisotropic "elasticity" of granular solids and provides a new framework to understand a large class of such systems.

### The elusive prediction of L-values

#### Prof. Loïc Merel

##### Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Paris Cité

An early wonder of our mathematical life happens when we come across the identity : $\sum_{n=1}^\infty \frac{1}{n^2} = \frac{π^2}{6}$. Even better, in Euler product form, $\prod_p \frac{1}{(1-1/p^2)} = \frac{π^2}{6}$, where p runs through the prime numbers. In the course of the ninetieth century, it appeared that the (zeta) function of a complex variable $ζ(s)=\sum_{n=1}^\infty \frac{1}{n^s}$, and its variants, is key to understand some of the subtle laws that govern prime numbers. Thus have the hearts of analytic number theorists been set beating. Meanwhile, algebraic number theorists have attempted to understand the meaning of "$\frac{π^2}{6}$". And, out of arithmetic geometry, they have defined a class of variants of ζ: the L-functions, series of the form $\sum_{k=1}^\infty \frac{a_k}{k^s}$ that can also be expressed as Euler products. Their valuations at integers produce the mysterious L-values, that we seek to understand. Well established conjectures now predict what the correct replacement for $\frac{π^2}{6}$ should be. But is the prediction complete? Contrary to what is often believed, not quite. Explanation for all this, including why elaborate conjectures still fall short, will not rely on general explanation of what L-functions are, but on illustrative examples based on elliptic curves and Dirichlet characters. An intriguing formula involving L-values will be offered to help reflect on the "not quite".

### Precision challenges in particle physics

#### Prof. Dr. Sven-Olaf Moch

##### Institut für Theoretische Physik, Universität Hamburg

We review the current state of precision predictions for the Large Hadron Collider LHC covering the aspects of perturbative corrections to hard scattering processes in quantum chromodynamics at higher orders as well as our knowledge on fundamental parameters of the Standard Model such as the strong coupling constant and heavy quark masses. We illustrate how the precision of available experimental data challenges current theoretical predictions and discuss the mathematical requirements needed to advance the latter. We present an outlook and outline areas for future improvements.

### What is Control Theory in 2021? Can AI do Better?

#### Prof. Olivier Pironneau

##### Member of the French Académie des Sciences

Until the twentieth century it was assumed that knowledge means control. Automatic control came in the sixties for electronics with Bellman's dynamic programming and Kalman's filter and received a boost in the eighties with robust and H∞ control. Will artificial intelligence algorithms change the practice of control drastically? Parallel Optimal Control, which dates from the calculus of variations of Hadamard and the Pontryagin principle is a more functional approach to the optimization of systems. It is heavily used for the design of mechanical devices like airplanes (optimal shape design) and the topological optimisation of materials. Stochastic control remained up to now a mathematical field except for the rare semi-analytical solutions as in the case of linear quadratic control. It is now computationally feasible and its applications to finance for instance, though challenged by deep neural networks, are in daily use for risk assessment of bank's portfolios. Finally, perhaps the most mathematically demanding is the mean-field type control and its application to the Monge-Ampere problem. As this is a colloquium talk, the problems and the main results will be stated only, without assuming any prior knowledge of these sometimes difficult fields. Yet the talk is for a mathematically trained audience.

##### Venue: Ramanujan Auditorium, IMSc