Welcome to my homepage! I am an Assistant Professor in the Department of Mathematics, IIT Bombay.
Graduate Students
Rahul Singh Karki is interested in commutative algebra and its interface with combinatorics.
Postdocs
Amit Roy at CEBS, Mumbai .
Rajib Sarkar at TIFR, Mumbai.
Postdoc Positions
Early career researchers with research interests in the combinatorial aspects of commutative algebra and algebraic geometry, broadly interpreted are encouraged to get in touch with me. We have several postdoctoral positions, please see the department webpage and the institute webpage . The duration of the postdoc can vary from 13 years.
As a postdoc at IITB, you are encouraged to take advantage of the large research groups in commutative algebra and algebraic geometry in Mumbai and actively participate in the seminars.
More about me
I was visiting the IHES, October 20December 2, 2017.
Earlier in 2017, I spent four months at the Erwin Schroedinger Institute for Mathematics and Physics, Vienna as a Junior Research Fellow and three months at the Mathematics Institute at Oberwolfach (MFO) as a Leibniz Fellow .
Until recently, I have been a postdoctoral researcher at the School of Mathematical Sciences at Queen Mary University of London and a Visiting Assistant Professor at the Mathematics Department at University of California Berkeley. My position in Berkeley was partially funded by FeoderLynen Fellowship of the Humboldt Foundation. My mentor was Prof. Bernd Sturmfels. Previously, I was a visiting assistant professor at the School of Mathematics, Georgia Institute of Technology where my mentor was Prof. Matt Baker.
News
20 March, 2023: Back to Mumbai after the Japan visit.
11 February, 2023: Going to Kyoto and Hyogo for workshops on hyperplane arrangements and lattice polytopes.
11 February, 2023: A one day commutative algebra workshop in Waseda university on February 6.
1 February, 2023: Just posted a preprint with a tropical application to nonHermitian physics: A Tropical Geometric Approach To Exceptional Points in collaboration with physicists at IISc.
10 May, 2022: Tutte Short Exact Sequences of Graphs has been accepted for publication in Combinatorial Theory.
10 May, 2022: The applications for the ICTS program “Combinatorial Algebraic Geometry – Tropical and Real” are open. Please apply!
14 November, 2021: BrillNoether Existence on Graphs via ℝDivisors, Polytopes and Lattices has been accepted for publication in Selecta Mathematica.
28 January 2021: I’ll participate in the semester program in combinatorial algebraic geometry at ICERM.
28 January 2021: Our (with Arvind Ayyer and Pranav Pandit) proposal for the two week workshop titled “Combinatorial Algebraic Geometry – Tropical and Real” has been accepted. The workshop is scheduled for June 27 – July 8, 2022.
3 December 2020: Here is video of a talk on Poincare Series of Divisors on Graphs.
25 November, 2020: Just posted a preprint “Poincare Series of Divisors on Graphs and Chains of Loops” to the arXiv.
March 30, 2020, Our (with Arvind Ayyer and Pranav Pandit) proposal for the two week workshop titled “Combinatorial Algebraic Geometry – Tropical and Real” July 12 – 23, 2021 at ICTS has been accepted. Details will be out in a bit. This workshop is scheduled right after FPSAC 2021 (July 59, 2021).
February 18, 2020, Visit to Japan from midApril to midMay, 2020 and will be based in Waseda University, Tokyo (host: Satoshi Murai). I also plan to visit Osaka and Kyoto. (March 30, 2020: has to be postponed because of the COVID 19 situation)
January 27, 2020, Obtained a MATRICS grant from SERB for the next three years (http://www.serb.gov.in/matrix.php).
January 27, 2020, I will be at ICTS 814 February for the workshop (https://www.icts.res.in/discussionmeeting/mbrs2020)
November 11, 2019, I am in the organising committee of FPSAC (http://fpsac.org/confs/fpsac2021/) to be held in IISc, Bangalore, July 521, 2021.
May 26, 2019, I will be in CIRM, Marseille June 1728, 2019 and then visit Ecole Polytechnique, Paris July 13, MPIMIS, Leipzig July 37.
March 13, 2019, Spencer Backman, Ye Luo and me will visit CIRM, Marseille on a research in pairs from June 1728, 2019.
November 30, 2018, Attended the 84th annual meeting of the Indian Mathematical Society in Jammu and Kashmir. Spoke at the session “Commutative Algebra and Algebraic Geometry”.
November 4, 2018, Attended the 84th annual meeting of the Indian Academy of Sciences in Varanasi.
July 4, 2018, Have been selected as an associate of the Indian Academy of Sciences .
June 25, 2018, The ATM school on Combinatorial Commutative Algebra last week was great fun! Sincere thanks to all the participants. Really enjoyed lecturing in it and listening to the other lectures. We’re currently preparing lecture notes that we plan to put up in the arxiv.
February 28, 2018, I’ll visit ICTP, Trieste, Italy for one month (May 15 June 15, 2018) under the Mathematics Visiting Fellowship.
December 20, 2017, Back to IITB after IHES visit, Pune conference on Commutative Algebra and Algebraic Geometry.
August 4, 2017, Currently in Bangalore, will join IITB midAugust. Visiting IHES, Paris October 20December 20, 2017.
July 6, 2017, We are planning to a start a seminar on “Combinatorial Aspects of Algebraic Geometry and Commutative Algebra” in IIT Bombay starting August, 2017. More details will follow soon.
May 23, 2017, I’ll be starting as an Assistant Professor in the Department of Mathematics, IIT Bombay from August 2017.
April 1, 2017, Commutative Algebra of Generalised Frobenius Numbers is on the arxiv.
January 8, 2017: I will spend time at MFO, Schroedinger Institute in Vienna and IHES Paris this year.
November 4, 2016: Back to London and expect to be here till the end of December.
October 24, 2016: Visiting Rice University, 26, 27 October and then Minneapolis for the AMS Special Session on “Chip Firing, Divisors on Graph and Simplicial Complex”, October 2830. My talk is on Saturday, 29 October.
October 6, 2016: We are holding a Tropical Geometry Seminar at Imperial this term. Our first meeting will be at Huxley 109, 4pm tomorrow (October 7). Please drop by or write to me if you want to know more about it.
September 13, 2016: Back to London and expect to be in this area throughout September.
August 1, 2016: Visiting India August 5September 7, 2016. I will visit TIFR, Mumbai, IIT Bombay and IIT Madras.
July 25, 2016: I am attending Latin American Algebra at Buones Aires, Argentina 2629 July. I’ll speak at the special session on Computational Algebra and Applications of Algebra on Friday 29 July.
July 20, 2016: I will visit MFO, Oberwolfach on a Leibniz Fellowship from JanuaryMarch 2017.
June 24, 2016: Syzygies over the Polytope Semiring is up on the arxiv.
Address
School of Mathematical Sciences,
Queen Mary University of London,
Mile End Road,
London, E1 4NS.
Research
My research interests are in the combinatorial aspects of algebraic geometry and commutative algebra. Specifically,
 Tropical and Nonarchimedean Geometry
 Combinatorial Commutative Algebra
 Algebraic Combinatorics
My google scholar page gives an impression of my papers. Here are some topics I have been working on.
 Commutative Algebra of BrillNoether Theory on Graphs:
We study BrillNoether theory on graphs from a commutative algebra point of view. We define modules on affine semigroup rings associated to graphs whose Hilbert series captures information related to special divisors on graphs.
 Tutte Short Exact Sequences Associated to Graphs:
We construct short exact sequences corresponding to Tutte deletioncontraction recurrences.
Other recent projects:
 Syzygies over Polytope Semirings:
Tropical geometry and its applications indicate a theory of syzygies over polytope semirings. The broad goal of this project is to developed this notion and study applications, for instance to canonical embeddings of tropical curves (as developed by Haase, Musiker and Yu) along the lines of Green’s study of syzygies of canonical algebra curves. I recently completed a paper that takes first steps in this direction.
 Tropical Graph Curves:
The broad goal in this project is to investigate the construction of “good” tropicalizations of canonical algebraic curves. More precisely, we mean tropicalizations that provide valuable information about the Berkovich analytification of the algebraic curve. This led to the concept of tropical graph curves. Using this we construct tropicalizations that capture the topology of the Berkovich analytification for algebraic curves whose graph underlying the Berkovich analytification is a threeconnected planar graph. See below for preprints.
 Commutative Algebra of Generalised Frobenius Numbers:
One goal of this project is to develop commutative algebraic interpretations of generalised Frobenius numbers. The combinatorial aspects have been developed in the work of Beck and Robins and the recent work of Aliev, De Loera and Louveaux. I have recently competed a paper with B. Smith in this direction.
Research Articles
2023
February
A Tropical Geometric Approach To Exceptional Points, Ayan Banerjee, Rimika Jaiswal, Madhusudan Manjunath and Awadhesh Narayan, 2023.
January
 Rational Normal Curves, Chip Firing and Betti Strata, Rahul Karki and Madhusudan Manjunath, 2023.
2020
 Poincaré Series of Divisors on Graphs and Chains of Loops, Madhusudan Manjunath, 2020.
2019
November
 BrillNoether Existence on Graphs via ℝDivisors, Polytopes and Lattices, Madhusudan Manjunath, Selecta Mathematica New Series 28 (35), 2022.
July

 Tropical Canonical Curves: the Planar Case, Madhusudan Manjunath, 2019. This is a revised version of the tropical graph curves preprint.
May
 Tutte Short Exact Sequences of Graphs, Madhusudan Manjunath, Combinatorial Theory 2(2), 2022.
2018
July
 Commutative Algebra of Generalised Frobenius Numbers, Madhusudan Manjunath and Ben Smith, Algebraic Combinatorics, 2018.
June
 Smoothing of Limit Linear Series of Rank One on
Saturated Metrized Complexes of Algebraic Curves , Ye Luo and Madhusudan Manjunath, Canadian Journal of Mathematics 70 (3), 628682. 2018.
2017
October
 Syzygies over the Polytope Semiring, Madhusudan Manjunath, Journal of the London Mathematical Society 96 (2), 2017, 482500 2017.
2016
 Tropical Graph Curves, Madhusudan Manjunath, March 2016.
January
 Embeddings and immersions of tropical curves, Dustin Cartwright, Andrew Dudzik, Madhusudan Manjunath, Yuan Yao, Collectanea Mathematica, Volume 67, Issue 1, pp 119, 2016.
2015 and Before:
 Explicit Deformation of Lattice Ideals via Chip Firing on Directed Graphs, Spencer Backman and Madhusudan Manjunath, Journal of Algebraic Combinatorics, Volume 42, Issue 4, pp 10971110, 2015.
 Minimal Free Resolutions of GParking Function Ideal and the Toppling Ideal, Madhusudan Manjunath, FrankOlaf Schreyer and John Wilmes, Transactions of the American Mathematical Society, Volume 367, pp 28532874, 2015.
 Monomial, Binomials and RiemannRoch,
Madhusudan Manjunath and Bernd Sturmfels, Journal of Algebraic Combinatorics, Volume 37, Issue 4, pp 737756, 2013.  The Laplacian Lattice of a Graph under a Simplicial Distance Function,
Madhusudan Manjunath, European Journal of Combinatorics, Volume 34,
Issue 6, pp 1051–1070, 2013.  The Rank of a Divisor on a Finite graph: Geometry and Computation., Madhusudan Manjunath, 2011 available in the arxiv at arXiv:1111.7251v1.
 Riemann Roch for sublattices of the Root Lattice An, Omid Amini and Madhusudan Manjunath, Electronic Journal of Combinatorics 17 (2010), Research Paper 124.
 Applications of Dimensionality Reduction and Exponential Sums to Graph Automorphism, Madhusudan Manjunath and Vikram Sharma, Theoretical Computer Science, Volume 412, Issue 29, pp 36393649, 2011.
 Approximate Counting of Cycles in Streams, Madhusudan Manjunath, Kurt Mehlhorn, Konstantinos Panagiotou and He Sun, the proceedings of the European Symposium on Algorithms (ESA), 2011.
 Minimizing Absolute Gaussian Curvature over Meshes, Joachim Giesen and Madhusudan Manjunath, Computational Geometry, Dagstuhl Seminar Proceedings 2009.
Dissertation
 RiemannRoch Theory for Sublattices of the Root Lattice An, Graph Automorphisms and Counting Cycles in Graphs, Madhusudan Manjunath, Dissertation, Saarland University
Teaching
In January 2016, I taught an LTCC course on Tropical Geometry. I previously taught introduction to Abstract Algebra, Math 113 in Berkeley. Previously, I have taught courses at both undergraduate and graduate levels. At the undergraduate level I have taught courses on linear and discrete mathematics and calculus at Georgia Tech and the graduate level a course on combinatorial commutative algebra at Saarland University.
Working with Students
As a postdoc, I have particularly enjoyed working with graduate
students and undergraduate students: mentoring, sharing my experiences with them and learning from them has been great fun! I look forward to working more with undergraduate and graduate students in the future.
Travelling
Some past travel
 AMS Fall Central Sectional Meeting, Special Session on ChipFiring and Divisors on Graphs and Complexes, October 2016.Recent Past
 Latin American Algebra, July 2016
 Tropical Day at Ecole Polytechnique, November 2015.
 Sandpile Groups at Banff, Oaxaca, Mexico, July 2016.
Nice to see you in class sir
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