Dr Dinakar Muthiah
- Senior Lecturer (Mathematics)
https://orcid.org/0000-0001-5580-1719Biography
Research interests
I work in Representation Theory and Algebraic Geometry. I am interested in geometric representation theory inspired by the Langlands program and mathematical physics. A few topics that particularly interest me: affine Grassmannians, p-adic groups, loop and double loop groups, Hecke algebras, intersection cohomology, Coulomb branches, symplectic varieties.
I am currently taking on PhD students, so please email me if you are interested in working in this area.
Research groups
Publications
2024
Muthiah, D. and Weekes, A. (2024) Fundamental monopole operators and embeddings of Kac-Moody affine Grassmannian slices. International Mathematics Research Notices, (doi: 10.1093/imrn/rnae115) (Early Online Publication)
2020
Muthiah, D. , Weekes, A. and Yacobi, O. (2020) On a conjecture of Pappas and Rapoport about the standard local model for GL_ d. Journal fur die Reine und Angewandte Mathematik (Crelles Journal), 772, pp. 175-185. (doi: 10.1515/crelle-2020-0030)
Muthiah, D. , Puskás, A. and Whitehead, I. (2020) Correction factors for Kac–Moody groups and t-deformed root multiplicities. Mathematische Zeitschrift, 296(1-2), pp. 127-145. (doi: 10.1007/s00209-019-02419-1)
Muthiah, D. , Weekes, A. and Yacobi, O. (2020) The equations defining affine Grassmannians in type A and a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman. International Mathematics Research Notices, 2022(3), pp. 1922-1972. (doi: 10.1093/imrn/rnaa131)
2019
Muthiah, D. and Orr, D. (2019) On the double-affine Bruhat order: the ε = 1 conjecture and classification of covers in ADE type. Algebraic Combinatorics, 2(2), pp. 197-216. (doi: 10.5802/alco.37)
2018
Muthiah, D. and Tingley, P. (2018) Affine PBW bases and affine MV polytopes. Selecta Mathematica - New Series, 24(5), pp. 4781-4810. (doi: 10.1007/s00029-018-0436-9)
Kamnitzer, J., Muthiah, D. and Weekes, A. (2018) On a reducedness conjecture for spherical Schubert varieties and slices in the affine Grassmannian. Transformation Groups, 23(3), pp. 707-722. (doi: 10.1007/s00031-017-9455-4)
Kamnitzer, J., Muthiah, D. , Weekes, A. and Yacobi, O. (2018) Reducedness of affine Grassmannian slices in type A. Proceedings of the American Mathematical Society, 146(2), pp. 861-874. (doi: 10.1090/proc/13850)
Muthiah, D. (2018) On Iwahori-Hecke algebras for p-adic loop groups: double coset basis and Bruhat order. American Journal of Mathematics, 140(1), pp. 221-244. (doi: 10.1353/ajm.2018.0004)
Muthiah, D. and Orr, D. (2018) Walk algebras, distinguished subexpressions, and point counting in Kac-Moody flag varieties. In: Representations of Lie Algebras, Quantum Groups and Related Topics. Series: Contemporary mathematics (713). American Mathematical Society: Providence, RI, pp. 187-203. ISBN 9781470436964
Articles
Muthiah, D. and Weekes, A. (2024) Fundamental monopole operators and embeddings of Kac-Moody affine Grassmannian slices. International Mathematics Research Notices, (doi: 10.1093/imrn/rnae115) (Early Online Publication)
Muthiah, D. and Weekes, A. (2023) Feuilles symplectiques pour les tranches dans les Grassmanniennes affines généralisées = Symplectic leaves for generalized affine Grassmannian slices. Annales Scientifiques de l'École Normale Supérieure, 56(1), pp. 287-298. (doi: 10.24033/asens.2534)
Muthiah, D. (2021) Weyl group action on weight zero Mirković-Vilonen basis and equivariant multiplicities. Advances in Mathematics, 385, 107793. (doi: 10.1016/j.aim.2021.107793)
Muthiah, D. , Weekes, A. and Yacobi, O. (2020) On a conjecture of Pappas and Rapoport about the standard local model for GL_ d. Journal fur die Reine und Angewandte Mathematik (Crelles Journal), 772, pp. 175-185. (doi: 10.1515/crelle-2020-0030)
Muthiah, D. , Puskás, A. and Whitehead, I. (2020) Correction factors for Kac–Moody groups and t-deformed root multiplicities. Mathematische Zeitschrift, 296(1-2), pp. 127-145. (doi: 10.1007/s00209-019-02419-1)
Muthiah, D. , Weekes, A. and Yacobi, O. (2020) The equations defining affine Grassmannians in type A and a conjecture of Kreiman, Lakshmibai, Magyar, and Weyman. International Mathematics Research Notices, 2022(3), pp. 1922-1972. (doi: 10.1093/imrn/rnaa131)
Muthiah, D. and Orr, D. (2019) On the double-affine Bruhat order: the ε = 1 conjecture and classification of covers in ADE type. Algebraic Combinatorics, 2(2), pp. 197-216. (doi: 10.5802/alco.37)
Muthiah, D. and Tingley, P. (2018) Affine PBW bases and affine MV polytopes. Selecta Mathematica - New Series, 24(5), pp. 4781-4810. (doi: 10.1007/s00029-018-0436-9)
Kamnitzer, J., Muthiah, D. and Weekes, A. (2018) On a reducedness conjecture for spherical Schubert varieties and slices in the affine Grassmannian. Transformation Groups, 23(3), pp. 707-722. (doi: 10.1007/s00031-017-9455-4)
Kamnitzer, J., Muthiah, D. , Weekes, A. and Yacobi, O. (2018) Reducedness of affine Grassmannian slices in type A. Proceedings of the American Mathematical Society, 146(2), pp. 861-874. (doi: 10.1090/proc/13850)
Muthiah, D. (2018) On Iwahori-Hecke algebras for p-adic loop groups: double coset basis and Bruhat order. American Journal of Mathematics, 140(1), pp. 221-244. (doi: 10.1353/ajm.2018.0004)
Book Sections
Muthiah, D. and Orr, D. (2018) Walk algebras, distinguished subexpressions, and point counting in Kac-Moody flag varieties. In: Representations of Lie Algebras, Quantum Groups and Related Topics. Series: Contemporary mathematics (713). American Mathematical Society: Providence, RI, pp. 187-203. ISBN 9781470436964
Supervision
- Dean, Lewis
Quantum integrable systems and TQFT - Lam, Shing Tak
The geometry of families of vector bundles