priyavrat deshpande

Chennai Mathematical Institute
SIPCOT IT park,Siruseri, TN 603103
+91 (044)6748 0962;
pdeshpande AT cmi DOT ac DOT in

I am an associate professor at the Chennai Mathematical Institute. I completed my PhD in 2011 in mathematics from University of Western Ontario, Canada under the supervision of Graham Denham and Ján Mináč. Then I spent a year at Northeastern in Boston followed by three years as a post-doc here at CMI. My mathematical interests broadly include Algebraic topology and Combinatorics. In particular I am interested in the theory of arrangements (hyperplanes, tori, submanifolds etc.), topological robotics and applications of algebraic topology.

I am one of the placement coordinators at CMI. If you are looking for hiring mathematicians to work in finance, machine learning, formal verification etc. feel free to write to me. Visit our placement page here.

I am also the local coordinator for the Madhava Mathematics Competition. If you are from around Chennai and are interested in participating in this competition then get in touch.

Research

Intially, right after the PhD, my research involves combinatorial and topological understanding of hyperplane arrangements. In my PhD thesis I initiated a study of submanifold arrangements. In particular I was interested in spherical, projective and toric arrangements. At some point in time I was also interested in topics like, discrete subgroups of diffeomorphisms that are generated by smooth involutions, right angled Artin groups etc.

Some of my recent projects were in topological robotics, including understanding of topology of planar polygon spaces, arachnoid mechanisms and navigational complexity of related spaces. I have also dabbled in enumerative combinatorics, topological combinatorics (in particular, shellability of certain graph complexes and also topological aspects of the Froberg's theorem).

These days I have taken a keen interest in exploring how techniques from data science and machine learning can be applied to topics in pure mathematics. In particular, I am working on certain problems related to elliptic curves, algebraic combinatorics and low-dimensional topology.

I was a recipient of SERB's MATRICS grant for the period of 3 years (June 2018 - March 2021).

Activities

  • I am one of the coorgianizer of Chennai Combinatorics Colloquium, a monthly talk series for combinatorics enthusiasts, in and around Chennai.
  • I am one of the coorganizers of OneMath World School on Topological Data Analysis to be held in February 2026. Link.
  • I am one of the coorganizers of BIRS-CMI workshop (January 2026) on Rigidity, Flexibility and Complexity of Geometric Constraint Systems. Link.
  • Arvind Ayyer and I organized an NCM workshop on "Topics in geometric combinatorics" in July 2025.
  • Pranabendu Misra, Siddharth Pritam and I organized a joint CS-Math workshop on applied topology and temporal graphs in CMI from Feb 5 to 9, 2024. webpage.
  • I and Anurag Singh organized an NCM funded workshop titled "Cohen-Macaulay complexes in graph theory" in CMI from 10-15 July, 2023. Visit the link for more details.
  • I and Dheeraj Kulkarni organized a 3-day meeting (July 16-18, 2018) for graduate students and postdocs interested in various aspects of topology. The details can be found here.
  • I co-organized Computational Geometry Day at CMI on 25/01/2018. For more information click here.
  • I and Ronno Das ran a weekly seminar on configuration spaces with a focus on understanding their cohomology as representations of the symmetric group. Webpage.

Publications

List of publications on arXiv
  1. Real Bott manifold structure of n-dimensional Klein bottle and its rational Betti numbers.
    (with N. Daundkar) Bol. Soc. Mat. Mex., 2025. arXiv, Journal
  2. Froberg's theorem, vertex splittability and higher independence complexes.
    (with A. Roy, A. Singh, A. Van Tuyl) J. Commut. Algebra 16(4): 391-410. arXiv, DOI
  3. On the structure of finitely presented Bestvina-Brady groups.
    (with M. Roy) Int. J. Algebra Comput. 34, No. 1, 69-85 (2024) DOI , arXiv.
  4. Building planar polygon spaces from the projective braid arrangement.
    (with N. Daundkar) Forum Mathematicum, 2024. DOI, arXiv.
  5. Chordal graphs, higher independence and vertex decomposable complexes.
    (with F. Abdelmalek, S. Goyal, A. Roy and A. Singh) Int. J. Algebra Comput. 33, No. 3, 481-498 (2023) DOI , arXiv.
  6. Refinements of the braid arrangement and two-parameter Fuss-Catalan numbers.
    (with K. Menon and W. Sarkar) J Algebr Comb (2022) DOI, arXiv.
  7. A branch statistic for trees: Interpreting coefficients of the characteristic polynomial of braid deformations.
    (with K. Menon) Enum. Comb. Appl. 3:1 Article S2R5, 2022. arXiv.
  8. The Borsuk-Ulam theorem for planar polygon spaces.
    (with N. Daundkar, S. Goyal and A. Singh), Topology Appl DOI. arXiv.
  9. On the topology of bi-cyclopermutohedra.
    (with N. Manikandan and A. Singh) Indian J. Pure Appl. Math. DOI and arXiv.
  10. Distance r-domination number and r-independence complexes of graphs.
    (with S. Shukla and A. Singh) Eur. J. Comb. 102, No. 103508 (2022), arXiv.
  11. The moment polytope of the abelian polygon space.
    (with N. Daundkar) Topology Appl. 302, Article ID 107834, 2021. arXiv.
  12. A combinatorial statistic for labeled threshold graphs.
    (with K. Menon and A. Singh) Enum. Comb. Appl. 1:3, Article S2R22, 2021. arXiv
  13. Counting regions of the boxed threshold arrangement.
    (with K. Menon and A. Singh) J. Integer Seq. 24, No. 5, Article 21.5.7, 2021. arXiv
  14. Higher Independence Complexes of graphs and their homotopy types.
    (with A. Singh) J.Ramanujan Math. Soc. 36, No. 1, 2021. arXiv
  15. Face counting formula for toric arrangements defined by root systems.
    (with K. Sutar) AKCE Int. J. Graphs Comb. 16, No. 1, 2019.
  16. Face enumeration for line arrangements in a 2-torus.
    (with K. Chandrashekhar) Indian J. Pure Appl. Math., 48(3), 2017.arXiv.
  17. On arrangements of pseudohyperplanes.
    Proc. Indian Acad. Sci. (Math. Sci.) Vol. 126, No. 3, 2016, pp. 399–420.
  18. Coxeter transformation groups and reflection arrangements in smooth manifolds.
    (with R. Das), J. Homot. Rel. Struct.,11:571-597, 2016, arXiv.
  19. Arrangements of spheres and projective spaces.
    Rocky Mountain J. Math 46(5): 1447-1487, 2016, link, arXiv.
  20. Deletion-restriction in toric arrangements.
    (with K. Sutar) J. Ramanujan Math. Soc. 31(1):17-30, 2016. arXiv.
  21. On a generalization of Zaslavsky's theorem for hyperplane arrangements.
    Ann. Comb., 18 (1):35-55, 2014. arXiv
Conference proceedings/ Extended abstracts
  1. A statistic for regions of braid deformations.
    (with K. Menon), Semin Lothar Combi 86B.23, proceedings of the 34th FPSAC, 2022. Link.
  2. Topology of permutation patterns.
    (with K. Menon, A. Singh), Permutation Patterns 2025. Link.
Accepted articles
  1. Sketches, moves and partitions: counting regions of deformations of reflection arrangements. (with K. Menon) To appear in Electronic Journal of Combinatorics arXiv.
Preprints
  1. Unveiling Arithmetic Statistics of Congruent Number Elliptic Curves via Data Science and Machine Learning (with A. Karnataki and P. Shingavekar) arXiv.
  2. The Goresky-MacPherson formula for toric arrangements arXiv.
  3. Arrangements of submanifolds and the tangent bundle complement arXiv.

teaching

In Aug - Nov 2025 I am teaching topological machine learning (2 credits) and topics in applied graph theory (2 credits)

Past courses

  1. Aug-Nov 2024 Mathematical Methods - Analysis
  2. Jan-Apr 2024 Linear algebra and its applications
  3. Aug-Nov 2023 Mathematical Methods - Analysis
  4. Jan-Apr 2023 Linear algebra and its applications
  5. Oct-Nov 2022 Enumerative combinatorics
  6. Aug-Nov 2022 Introduction to manifolds
  7. Mar-Apr 2022 Graduate topology 2
  8. Jan-Feb 2022 Topological data analysis
  9. Sep-Dec 2021 Intro to manifolds
  10. Apr-Jul 2021 Algebra 2
  11. Mar-Apr 2021 Topological data analysis
  12. Aug-Nov 2020 Differential topology
  13. Jan-Apr 2020 Graduate complex analysis
  14. Aug-Nov 2019 Topological data analysis
  15. Jan-Apr 2019 Graduate Topology 2
  16. Aug-Nov 2018 Topological Robotics.
  17. Aug-Nov 2018 Intro to Manifolds.
  18. Jan-Apr 2018 Topics in combinatorics .
  19. Aug-Nov 2017 Intro to Manifolds
  20. Jan-Apr 2017 Graduate Topology 2
  21. Aug-Nov 2016 Combinatorics 1
  22. Aug-Nov 2015 Homotopy theory
  23. Jan-Apr 2015 Differential topology
  24. Jan-Apr 2015 Topics in topology
  25. Aug-Nov 2014 Algebraic topology
  26. Jan-Apr 2014 Algebraic topology II
  27. Aug-Nov 2013 Algebraic topology
  28. Jan-Apr 2013 Intro to reflection groups.
  29. Aug-Nov 2012 Real analysis

supervision

Postdoc
  1. Sagar Sawant (December 2024-July 2025): PhD (2024) from IIT Madras.
  2. Amit Roy (January 2024-present): PhD (2020) from IISER, Mohali.
  3. Mallika Roy (2021-2022): PhD (2020) from Universitat Politecnica de Catalunya. Currently an NBHM postdoctoral fellow at HRI.
  4. Shuchita Goyal (2019-2021): PhD (2019) from IIT Bombay. Currently a faculty at BITS Pilani.
  5. Anurag Singh (2018-2021): PhD (2018) from IIT Kanpur. Currently a faculty at IIT Bhilai.
PhD students
  1. Rutuja Sawant (2024-present). Working on topology of graph complexes.
  2. K. Menon (2021-2025). He defended his thesis in January 2025 and then joined KTH, Sweden as a postdoc.
  3. N. Daundkar (2017-2022). Currently an INSPIRE faculty at IISER, Pune (thesis).
MSc students
  1. Deepak M.S. (2021-22): Topological complexity (thesis).
  2. Shambhavi S. (2020-21, IISER Pune): Applications of topology to data analysis (thesis).
  3. Krihna Menon (2020-21): Counting regions of the deformations of the braid arrangement (thesis).
  4. Sahil Kulasreshtha (2019-20): Information cohomology.
  5. Naageswaran M. (2018-19): On the topology of cyclopermutohedron and its quotient (thesis).
  6. Nachiketa Adhikari (2016-17): Discrete Morse theory on moduli spaces of planar polygons (thesis).
  7. Abhishek Khetan (2015-16): A cellular model for the configuration space of points on graphs (thesis).
  8. Ronno Das (2014-15): Salvetti complex construction for manifold reflection arrangements (thesis).
  9. Karthik C. (2013-14): Face numbers of toric arrangements.

Misc.

Links

Kavita Sutar
Alex Suciu
Graham Denham
Ján Mináč
Jnana Prabodhini, India