Talks

The characterization of identical quantum particles as bosons or fermions goes back to the early days of quantum mechanics. It was realized much later that in two space dimensions, particles with any statistics (`anyons') can exist. Such particles can emerge as quasiparticles in quantum phases of matter. The prime experimental example is in the Fractional Quantum Hall Effect (FQHE). After a brief review of the FQHE, I will discuss recent developments on the observation of the phenomenon in zero magnetic field, and the associated questions and opportunities.

Microbial ecosystems frequently exhibit multiple alternative stable states under identical environmental conditions, separated by abrupt regime shifts. These shifts complicate the understanding, manipulation, and control of such systems, with significant implications for natural, industrial, and health-related contexts. In this talk, I present a unified framework combining insights from nutrient competition and phage-bacteria interactions to explore these dynamics.
First, I will discuss models that predict stable states in microbial ecosystems based on different resource utilization strategies. The first model [1] describes communities of diauxically growing microbes, where species dynamically switch between nutrient preferences depending on environmental availability. In contrast, the second model [2] focuses on specialist species, each limited by two essential nutrients, such as carbon and nitrogen, represented by multiple metabolites. Both models draw inspiration from the stable marriage problem in economics, developed by Gale and Shapley in the 1960s and awarded the Nobel Prize in Economics in 2012. Using ranked tables of species' competitive abilities for nutrients, these models identify all feasible stable states and the specific environmental conditions—characterized by nutrient fluxes—where they occur. This framework reveals a complex network of transitions between stable states and highlights perturbations that induce regime shifts versus those with transient effects.
Next, I address alternative stable states in phage-bacteria systems, building on the findings in [3]. These systems demonstrate how bacterial growth rates, phage burst sizes, and defense mechanisms like CRISPR and abortive infection drive regime shifts. For example, a fast-growing bacterium may exclude slow-growing one via nutrient depletion, but phage predation can invert this dynamic, favoring the slower-growing bacterium.
References:
[1] Goyal A, Dubinkina V, Maslov S. Multiple stable states in microbial communities explained by the stable marriage problem. ISME J. 2018;12: 2823–2834. https://doi.org/10.1038/s41396-018-0222-x
[2] Dubinkina V, Fridman Y, Pandey PP, Maslov S. Multistability and regime shifts in microbial communities explained by competition for essential nutrients. eLife. 2019;8:e49720. https://doi.org/10.7554/eLife.49720
[3] Maslov S, Sneppen K. Regime shifts in a phage-bacterium ecosystem and strategies for its control. mSystems. 2019;4:e00470-19. https://doi.org/10.1128/mSystems.00470-19

Quantum physics has reshaped our understanding of materials and created opportunities to design materials for novel device applications. For example, superconductivity, an emergent quantum phenomenon in which electrons move without dissipating energy, has been exploited for devices that enable quantum computing and communications. In addition, modern electronics rely heavily on technology that confines electrons in the interfacial layers of atoms, where the electrons move in an effective two-dimensional (2D) space, a flatland. The unique properties of these low-dimensional material systems are generally understood by considering enhanced quantum effects. In recent years, scientists have discovered that they can stack atomically thin 2D quantum materials to create engineered materials with a wide variety of electronic and optical properties. In this talk, we will discuss several research efforts to realize emergent physical phenomena in stacked atomically thin layered materials and possible applications based on these materials.

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