Search Talks

Physicists have been trying to develop a theory that puts together general relativity and quantum mechanics. We will highlight some interesting theoretical ideas and point out a couple of concrete predictions.

Computation is built on the fundamental laws of physics. At its heart, computation is a dance of countless interacting particles — what physicists call a many-body system — whether the computation is done by classical bits in a chip or qubits in a quantum processor. In this lecture, I will explore how ideas from many-body physics have shaped the past, present, and future of computation: from the collective behavior of electrons in semiconductors, to the spin-glass theory breakthroughs, like Hopfield neural networks, which laid the foundation for artificial intelligence and machine learning, to the importance of topological phases in enabling robust error correction for quantum processors.

We are now at the cusp of a new quantum era. Advances in quantum engineering provide unprecedented control over many-body systems, opening up entirely new frontiers for exploring quantum matter. These quantum devices allow us, for the first time, to study non-equilibrium many-body quantum systems, where novel dynamical phases — like time crystals — emerge. They also enable the creation of tunable and coherent quantum networks, leading to new phases in non-Euclidean geometries — such as topological quantum spin glasses. Beyond advancing our understanding of quantum matter, these developments are inspiring innovative paradigms for error correction, including Floquet codes and LDPC expander codes, which could transform the landscape of quantum computation.

Together, these developments reveal the profound connections between physics, information, and computation, paving the way for advances that will define the next 100 years of quantum mechanics.

Ecology is a very fragmented field with a variety of scientific questions and cultures. Toward the end of the school, I will present a personal perspective on what red threads run through the whole field and when the connection can benefit or not from being made in a mathematical language.

1. Phenomenology of community variability (intro, SAD)
2. Phenomenology in microbial communities (minimal patterns)
3. demographic stochasicity and migrations (birth-death-migration)
4. flavours of neutral theory (assumption, predictions)
5. continuous limit of birth-death-migration process (stationary and dynamic solution)
6. when NT works and fails

The gauge/gravity duality maps strongly correlated quantum condensed matter systems onto holographic models of gravity and provides a non-perturbative approach towards predicting its transport properties. In graphene, when the electron-electron scattering becomes more frequent than the scattering of electrons by phonons or disorder, the electrons gas behaves as a hydrodynamic fluid and expected to exhibit emergent universalities in dc charge and heat transport close to the charge neutrality where graphene becomes quantum critical. In this talk, I shall present some new experimental result on the electrical and thermal transport measurements in extremely high-quality graphene devices. I shall give evidence of the universal dc transport, breakdown of the Widemann-Franz law, and approach to the holographic limit of minimally dissipative flow of charge. We believe these experiments will lead to a new strategy to exploit high-quality graphene as a testing bed for some of the unifying concepts in physics.

While the formulation of quantum mechanics predates computability theory, the idea of computers based on quantum physics only arose much later, in the 1980s. Initially studied only by the curious and intrepid, quantum computation, and quantum information processing in general, came into the limelight in the 1990s. The impetus, namely, the discovery of rigorous evidence of the advantage offered by quantum computers, culminating in the Shor algorithm for Integer Factorization, is now well-known. Since then, the field has been guided by the promise of new technology while also allowing for the pursuit of ideas unfettered by practical (or even physical) considerations. I will describe some of the advances in the field in the wake of these developments.

Another important interdisciplinary approach in ecology is the search for large-scale or even "universal" empirical patterns with simple explanations, such as distribution of energy and biomass across the world and across various types of organisms (plants, herbivores, carnivores...). This lecture will present some insights and limits of simple deterministic patterns constrained by biological mechanisms.

Understanding the semiclassical limit of the quantization of even the simplest classically chaotic Hamiltonian, proved to be problematic from the inception of quantum mechanics 100 years ago. Arithmetically defined such systems provide instances for which this limit can be analyzed mathematically using central tools from number theory and homogeneous dynamics.As such these can be thought of as "solvable models ". We review some of the many developments for these quantizations.

1. basics on RV (probability, moments, mgf, continuous RVs)
2. summing RVs and central limit theorem
3. sampling (binomial, poisson)
4. intro on stochastic processes
5. random walk
6. birth-death process (basics and exctintiion)
7. birth-death-migration process (stationary probability)

In 1924, Bose communicated a derivation of the Planck distribution, to Einstein, where Bose introduced a key notion of indistinguishability of photon quanta. This was a turning point in the history of quantum mechanics. Bose's article is considered the fourth most important article, in the development of quantum mechanics, following those of Planck, Einstein and Niels Bohr. It was Dirac, who coined the names Bosons and Fermions.  We present a brief historical account of Bose’s discovery, followed by a bird’s eye view of the impacts of boson bloom and Bose-Einstein condensation in modern science and technology.

[1] Boson Bloom, G. Baskaran and A. May, J. Physics B, 57, 142001 (2024)