Theoretical Statistics and Mathematics Unit

## Seminar and Colloquium of the week

### STUDENT SEMINAR

Title : Statistical physics and statistics in understanding dynamics of ecological systems
Speaker : Vishwesha Guttal (Center for Ecological Sciences IISC)
Time : September 18, 2018 (Tuesday), 03:00 PM
Venue : Platinum Jubliee Auditorium
Abstract : Ecosystems can be viewed as complex dynamical systems where a large number of living organisms interact to produce many emergent patterns. In this talk, I will demonstrate some examples of ecological phenomena where principles of nonequilibrium statistical mechanics, bifurcation theory together with statistical tools of data analyses offer novel insights and predictive power in our understanding of ecology. Specifically, I present examples of tipping points where ecosystems can abruptly switch to a state with contrasting features. Commonly cited empirical examples of tipping points are desertification in semi-arid ecosystems, algal blooms in aquatic ecosystems, paleo-climatic shifts, and crashes in financial markets. More recently, these ideas have also been applied in genetic circuits and regulatory networks. By drawing an analogy to physics of phase transitions, I will present how one can devise early warning signals of such tipping points. I will discuss empirical evidence for these theoretical predictions from savanna and desert ecosystems, lakes as well as financial markets. If time permits, I will also talk about collective behaviour in animal groups where one finds spectacular forms of synchrony in moving animal groups.

### COLLOQUIUM

Title :Conformal field theory; vertex operator algebras and some problems
Speaker : Robin Hillier (Lancaster University)
Time : September 20, 2018 (Thursday), 03:30 PM
Venue : Auditorium
Abstract : The talk will start with an elementary introduction to conformal quantum field theory, its achievements and some of its mathematical ambiguities. There are mainly two frameworks to overcome those ambiguities, which are actually of independent interest -- one is called vertex operator algebras, the other one is called nets of von Neumann algebras. I will sketch how they arise and what they are good for. We will also look at examples and attempts of classification. The technical details shall be kept to a minimum.

### STUDENT SEMINAR

Title : Beyond the walls of schooling
Speaker : Jane Sahi (Azim Premji University Bangalore)
Time : September 25, 2018 (Tuesday), 03:15 PM
Venue : Platinum Jubliee Auditorium
Abstract : I would like to share some reflections on my involvement with alternative education over a number of years. What does ‘alternative’ in relation to schooling mean in the present climate of growing commercialization, bureaucratization and changing aspirations? How can we prepare children for a more just and inclusive society?

### COLLOQUIUM

Title :Vector-valued Tietze's extension theorem for compact domains-A geometric approach
Speaker : T.S.S.R.K. Rao (Indian Statistical Institute - Bangalore)
Time : September 27, 2018 (Thursday), 03:30 PM
Venue : G25
Abstract : Let $\Omega$ be a compact Hausdorff space and let $E \subset \Omega$ be a closed subset. Let $X$ be a Banach space and let $C(\Omega,X)$ be the space of $X$-valued continuous functions on $\Omega$ equipped with the supremum norm. We first give a geometric proof of the known result, functions in $C(E,X)$ have norm preserving extensions in $C(\Omega,X)$. Let $K$ be a Compact Choquet simplex and let $A(K,X)$ denote the space of affine continuous functions on $K$, equipped with the supremum norm. We extend Tietze's theorem to compact sets contained in the extreme boundary of $K$.

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