Abhishek Deshpande

B2-304 Vindhya, IIIT Hyderabad,

Prof. CR Rao Road, Gachibowli,

Hyderabad 500032,

Telangana, India

Email: abhishek.deshpande@iiit.ac.in

Phone: (+91) 040 6653 1000

News: SERB- Startup Research Grant (SRG) awarded to work on "Dynamical equivalence of reaction networks"

Professional Trajectory:

2021 - Assistant Professor,

Center for Computational Natural Science and Bioinformatics,

IIIT Hyderabad, India

2018 - 2021 Van Vleck Visiting Assistant Professor,

University of Wisconsin Madison (Postdoctoral mentor: Gheorghe Craciun)

2014 - 2018 PhD in Applied Mathematics,

Imperial College London (Advisors: Manoj Gopalkrishnan, Thomas Ouldridge and Nick Jones)

2009 - 2014 B.Tech in Computer Science and M.S in Computational Natural Science,

IIIT Hyderabad, India.

My research lies at the interface of Dynamical systems, Chemical reaction networks, Biological Computation, Physics of Computation, Polyhedral geometry and Oriented Matroids.

Reaction networks model the interaction between species. They can be visualized as finite graphs embedded in Euclidean space. The key idea is to relate the dynamics of the reaction network with its underlying structure. In particular, can a particular species not go extinct in the system? Another related question is whether solutions of a trajectory eventually converge to a compact set? A thread of my research uses the theory of reaction networks pioneered by Horn and Jackson to answer such questions.

Using biological networks for performing computation has been a topic of interest ever since Adleman's ingenious solution of the Hamiltonian path problem using DNA strands. Taking this further, we seek to use the power of reaction networks to perform inference and computation. The idea here is to exploit the dynamics exhibited by reaction networks to mimic algorithms in machine learning and artifical intellegence.

There exists fundamental lower bounds on the energy costs required for performing information processing in bits. In particular, there exists an energy lower bound of kTlog(2) for erasing bits in the quasi-static limit. If we insist that bits be erased fast (in finite time) and require that they store information for a long periods of time (be reliable), then a substantially large energy cost is required. In particular, we study how to design optimal bits - bits that can store information for a long period of time and can be erased fast at a minimal cost.

Models of biological systems can often be expressed as a system of polynomial equations i.e., as affine algebraic varieties. In particular, these networks are known to exquisite behaviour like multistationarity, oscillations and Hopf bifurcations. A thread of my research uses techniques from algebraic geometry, polyhedral geometry and the theory of oriented matroids to analyze the polynomial systems that are responsible for this exotic behaviour.