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Research Interest Combinatorial Commutative Algebra

Courses at IIT Hyderabad I have taught the following courses

Aug-Dec 2021 - Linear Algebra (MA4020) ongoing.

Jan-April 2021 - Introduction to Lattice Theory (MA3050).

Nov 2020 - Feb 2021 - Combinatorics (MA1240).

Aug-Dec 2020 - Introduction to Group Theory (MA2070), Combinatorics and Graph Theory (MA5010).

Jan-April 2020 - Complex Analysis (MA4060), Vector Calculus (MA1130).

Aug-Dec 2019 - Commutative Algebra (MA6116), Combinatorics and Graph Theory (MA5010).

Jan-April 2019 - Differential Equations (MA1150).

Ph.D. seminar courses Combinatorial Commutative Algebra (MA6126), Homological Algebra II (MA4150), Computational Algebra on Polynomials and Ideals (MA4133).


Teaching Excellence Award 2021 (by IIT Hyderabad)

Education

PhD in Mathematics and Applications  ‒  University of Genova,  Italy,  (May 2014).

Thesis: Koszul property of diagonal subalgebras and complete intersections of symmetric polynomials, (Advisor: Prof. Aldo Conca).

M.Sc Mathematics  ‒  University of Hyderabad, (June 2008).

B.Sc Mathematics  ‒  St. Xavier's college Ranchi, (June 2005).

Publications

Diagonal Subalgebras of Residual Intersections  ‒ (with H. Ananthnarayan, and Vivek Mukundan), Proc. Amer. Math. Soc., (148) 2020, no. 1, 41-52.

A survey on Koszul algebras and Koszul duality  ‒  Proceedings of Leavitt Path Algebras and Classical K-Theory, Indian Statistical Institute Series, Springer Nature Singapore Pte Ltd., ISSN 2523-3114, pp xxi+ 322, 2020.

Syzygies, Betti numbers, and Regularity of cover ideals of certain multipartite graphs  ‒ (with A.V. Jayanthan), Mathematics, 7(9), 2019, 1-18, 869.

Note on vanishing power sums of roots of unity  ‒  (with K. Senthil Kumar) The Mathematics Student (84) 2015, no. 3-4, 69-73.

Koszul property of diagonal subalgebras  ‒  Journal of Commutative Algebra (6) 2014, no. 3, 385-406.

Quillen-Suslin theory for a structure theorem for the Elementary Symplectic Group ‒  (with Ravi A. Rao) Ramanujan Math. Soc. Lect. Notes Ser. (17) 2013, 101-116.

Regular sequences of power sums and complete symmetric polynomials ‒  (with Ivan Martino) Le Matematiche (Catania) (67) 2012, no. 1, 103-117.

An algebraic proof for the identities for degree of syzygies in numerical semigroups  ‒  (with Ivan Martino) Le Matematiche (Catania) (67) 2012, no. 1, 81-89.

Research experiences and employments

IIT Bombay  ‒  Postdoctoral fellow (November 2016  ‒  January 2019).

ISI Bangalore  ‒  Visiting Scientist (June 2016  ‒  Sep 2016).

IMSc Chennai  ‒  Postdoctoral fellow (April 2014  ‒  June 2016).