## IGERT Summer Institute 2017

**Schedule**

All talks take place in Abelson 229

Break each day: 11 - 11:30 am

Lunch each day: 12:30 pm (ordered in)

**Wednesday, May 31**

- 10 - 11 am,
**Yiting Li**(Brandeis University)

**Title:**"Introduction to some basic background of random matrix"

**Abstract:**In this talk I will introduce some basic concepts and results in the random matrix theory. They will include: GOE, GUE, Wigner's semicircle law, Tracy-Widom distribution. If time allows I will also introduce the universality of Wigner matrix and the circular law.

- 11:30 am - 12:30 pm,
**Robert Marsland**(MIT)

**Title:**"The Edge of Thermodynamics: Driven Steady States in Physics and Biology" PDF of Marsland's talk here

**Abstract:**From its inception, statistical mechanics has aspired to become the link between biology and physics. But classical statistical mechanics dealt primarily with systems in thermal equilibrium, where detailed balance forbids the autonomous directed motion characteristic of living things. Significant theoretical effort has been expended in the last twenty years to extend thermodynamic formalism to encompass nonequilibrium structures, which are sustained by a constant flux of matter or energy. This generalization is most promising in ergodic systems, which reach a steady state in finite time that is independent of the initial condition. In my talk, I will address two basic questions about these driven steady states: Under what conditions does nonequilibrium thermodynamics tell us something new about their measurable properties? And what design goals can be achieved in these states that are impossible at equilibrium?

**Thursday, June 1**

- 10 - 11 am,
**Carl Merrigan**(Brandeis University)

**Title:**"Introduction to First Passage Times"

**Abstract:**A common statistical question that can come up is to ask what will be the the distribution of times taken for some event of interest to occur for the very first time. For instance, at what time will a neuron first fire or at what time will a stock value reach a certain threshold. First passage time questions can be dealt with exactly for many scenarios involving simple random walks and/or continuum diffusion processes. In this talk, I will give an introduction to the techniques involved by outlining the steps in calculating the first passage time distribution for a 1d lattice random walk. I will also indicate how the continuum version of the same result can be derived.

- 11:30 am - 12:30 pm,
**Yiting Li**(Brandeis University)

**Title:**"Rigidity of eigenvalues for beta ensemble in multi-cut regime" PDF

**Abstract:**I will first talk about the background and some well known results of beta ensemble. Then I will introduce the rigidity of eigenvalues for beta ensemble in multi-cut regime, i.e., the fact that each eigenvalue in the bulk is very close to its "classical location". The probability that the distance between the eigenvalue and its classical location is larger than N^{-1+r} is exponentially small where r is an arbitrarily small positive number. The model is an generalization of the beta ensemble in one-cut regime for which the rigidity of eigenvalues was proved by Bourgade, Erdos and Yau. This is the work of my thesis.

**Friday, June 2**

- 10 - 11 am,
**Xiaoming Mao**(University of Michigan)

**Title: "**Maxwell lattices and topological mechanics"

**Abstract:**In this short course I will introduce the new field of topological mechanics. I will start from basics of Maxwell lattices which are mechanical structures at the verge of instability, and discuss the recent literature of using these lattices to the study of soft matter systems. Then I will discuss how the topology of the phonon band structure of these Maxwell lattices lead to the interesting phenomena of topological floppy edge modes in these lattices, which give rise to reconfigurable asymmetric edge stiffness, with potential applications in materials science.

- 11:30 am - 12:30 pm,
**Joe Rauch**(Brandeis University)

**Title: "**Public goods production counters niche competition and enables multi-species coexistence"

**Abstract:**Traditional theoretical ecology has difficulty explaining the large amount of diversity observed in natural microbial communities. Due to observations of frequency dependent growth of microbes in the presence of an essential public good, we investigated the public good game’s influence on the diversity of microbial communities. We find the public good game reproduces both low and highly diverse communities. Additionally, the model predicts other observed features of microbial communities, including key stone species, a functional cache, and equilibrium dependence on initial colonization.

- 1:30 - 2:30 pm,
**Xiaoming Mao**(University of Michigan)

**Title: "**Maxwell lattices and topological mechanics"

**Abstract:**In this short course I will introduce the new field of topological mechanics. I will start from basics of Maxwell lattices which are mechanical structures at the verge of instability, and discuss the recent literature of using these lattices to the study of soft matter systems. Then I will discuss how the topology of the phonon band structure of these Maxwell lattices lead to the interesting phenomena of topological floppy edge modes in these lattices, which give rise to reconfigurable asymmetric edge stiffness, with potential applications in materials science.

**Monday, June 5**

- 10 - 11 am,
**Todd Gingrich**(MIT)

**Title:**"Dynamical fluctuations in Markov processes - A Primer on Stochastic Thermodynamics, Fluctuation Theorems, and Large Deviations"

**Abstract:**The dynamics of many physical systems may be modeled using Markov processes, and the statistical irreversibility of those Markov processes can be related to the nonequilibrium thermodynamics of the system (heat flow, particle flux, etc. supplied by external reservoirs). I will first review this Stochastic Thermodynamic framework then will introduce tools from Large Deviation Theory to analyze the dynamical fluctuations of Markov processes. Using these large deviation methods we will derive the entropy production fluctuation theorem as well as the more recently discovered "thermodynamic uncertainty principle" for fluctuating nonequilibrium currents.

- 11:30 am - 12:30 pm,
**Lishibanya Mohapatra**(Brandeis University)

**Title:**"How cells control the size of their organelles?"

**Abstract:**Cells contain a number of micron-scale structures, whose physiological functions are related to their size. Examples include cytoskeletal elements like mitotic spindle, cilia and actin cables. Each of these structures is characterized by a narrow size distribution and is composed of molecular building blocks (tubulin dimers and actin monomers) that diffuse in the cytoplasm. A key question in cell biology is how the size of these structures is maintained in light of constant turnover of their molecular components. Using theory, simulations and experiments in various cell types, I will describe how we can aim to uncover design principles of size-control in biology.

**Tuesday, June 6**

- 10 - 11 am,
**Brad Marston**(Brown University)

**Title:**"El Niño as a Topological Insulator: A Surprising Connection Between Climate, and Quantum, Physics”

**Abstract:**Symmetries and topology play central roles in our understanding of physics. Topology explains the precise quantization of the Hall effect and the protection of surface states in topological insulators against scattering from disorder or bumps. However discrete symmetries and topology have so far played little role in thinking about the fluid dynamics of oceans and atmospheres. I show that, as a consequence of the rotation of the Earth that breaks time reversal symmetry, equatorially trapped Kelvin and Yanai waves emerge as topologically protected edge modes. Thus the oceans and atmosphere of Earth naturally shares basic physics with topological insulators. As equatorially trapped Kelvin waves in the Pacific ocean are an important component of El Niño Southern Oscillation, these new results demonstrate that topology plays a surprising role in Earth’s climate system.

- 11:30 am - 12:30 pm,
**Todd Gingrich**(MIT)

**Title:**"Dynamical fluctuations in Markov processes - A Primer on Stochastic Thermodynamics, Fluctuation Theorems, and Large Deviations"

**Abstract:**The dynamics of many physical systems may be modeled using Markov processes, and the statistical irreversibility of those Markov processes can be related to the nonequilibrium thermodynamics of the system (heat flow, particle flux, etc. supplied by external reservoirs). I will first review this Stochastic Thermodynamic framework then will introduce tools from Large Deviation Theory to analyze the dynamical fluctuations of Markov processes. Using these large deviation methods we will derive the entropy production fluctuation theorem as well as the more recently discovered "thermodynamic uncertainty principle" for fluctuating nonequilibrium currents.

**Wednesday, June 7**

- 10 - 11 am,
**Todd Gingrich**(MIT)

**Title:**"Dynamical fluctuations in Markov processes - A Primer on Stochastic Thermodynamics, Fluctuation Theorems, and Large Deviations"

**Abstract:**The dynamics of many physical systems may be modeled using Markov processes, and the statistical irreversibility of those Markov processes can be related to the nonequilibrium thermodynamics of the system (heat flow, particle flux, etc. supplied by external reservoirs). I will first review this Stochastic Thermodynamic framework then will introduce tools from Large Deviation Theory to analyze the dynamical fluctuations of Markov processes. Using these large deviation methods we will derive the entropy production fluctuation theorem as well as the more recently discovered "thermodynamic uncertainty principle" for fluctuating nonequilibrium currents.

- 11:30 am - 12:30 pm,
**Rose Morris-Wright**(Brandeis University)

**Title:**"Generalizing Hyperbolic Space and its Groups of Isometries"

**Abstract:**Historically, hyperbolic geometry has been a rich area of research for mathematicians and physicists. To generalize this theory, consider metric spaces which have many of the same properties as classical hyperbolic space, but which are not necessarily Remannian manifolds. I will introduce these hyperbolic-like spaces, as they were proposed by Gromov in 1983. I will then discuss some of the consequences of this theory for abstract algebra and group theory. Finally, I will discuss some further generalizations which are currently being studied, especially the concept of acylindrical hyperbolicity as defined by Osin in 2016.

**2016**

**Speakers:**

- Daniel Goldstein (Brandeis University) ”A Kinetic Model of Active Extensile Bundles"
- Julian Butcher (Brandeis University) "A Continuum Theory of Active Nematics in a Bounded, Two Dimensional System"
- Sumantra Sarkar (MIT) “Force Tiling: Finding patterns in the forces"

- Geoffrey Conklin (Brandeis University) "Chemical Modelling with Semi-Classical Valence Electrons"
- Paul Miller (Brandeis University) "From the Ising model to cognition: exploring attractor states in neuroscience"
- Benjamin Hancock (Brandeis University) "Statistical Mechanics and Hydrodynamics of Self-Propelled Hard Spheres"
- Biji Wong (Brandeis University) "Turaev torsion & Seiberg-Witten invariants of 3-orbifolds"

2015

2015

**Speakers**:

- Sumit Das (University of Kentucky) "Quantum Quench and Holography" Lecture Notes
- Chandan Dasgupta (IISC, Bangalore) "Introduction to spin glasses and structural glasses"
- Rajesh Gopakumar (HRI, Allahabad and ICTS) "Vector Models at large N and Holography" Lecture Notes
- Alex Maloney (McGill University) "AdS/CFT, Quantum Entanglement and Quantum Gravity"
- Kabir Ramola (Brandeis University) "Extreme Value Statistics and Some Applications to Disordered Systems"
- Sanjib Sabhapandit (Raman Research Institute, Bangalore ) "Fluctuations and large deviations in nonequilibrium systems" Lecture Notes
- Peter Weichman (BAE Systems) "Geophysical Fluid Dynamics: A Statistical Physics Laboratory" Lecture Notes
- Paul Chesler (Harvard University) "Gravitational collapse, holography, and hydrodynamics in extreme conditions" Lecture Notes

**Student Speakers:**

- Cesar Agón (Brandeis University) "Entanglement Entropy in Quantum Field Theory and Holography" Lecture Notes
- Benjamin Hancock (Brandeis University) "Pressure and Self-Propelled Particles" Lecture Notes
- Carl Merrigan (Brandeis University) "KEP Model for Soft Glassy Materials" Lecture Notes

- Lishibanya Mohapatra (Brandeis University) "How cells control the size of their organelles" Lecture Notes