Workshop on Group Theory 2026

Speakers (Title and Abstracts of Talks):

1. Sumana Hatui, NISER Bhubaneswar

Title: On faithful projective representations of finite groups and their minimal dimension

Abstract:  In this talk, we discuss faithful projective representations of finite groups and the problem of finding their minimum possible dimension. For finite p-groups, we give a cohomological criterion for a 2-cocycle to admit a faithful irreducible projective representation. Then we introduce the projective embedding degree and the irreducible projective embedding degree of a finite group. We discuss these invariants for some important classes of groups, including finite abelian groups, extraspecial p-groups, Heisenberg groups, and groups of small prime-power order.

2. Sunil Kumar Prajapati, IIT Bhubaneswar

Title:  Character codegrees and exceptional groups

Abstract

3. Ayush Udeep, SRM Institute of Science and Technology Kattankulathur, Chennai 

Title: Character codegree of finite p-groups

Abstract:  The character codegree of an irreducible character of a finite group G is given by the index of its kernel in G upon the character degree. The character codegree set, denoted $\cod(G)$, is the set of the codegrees of all irreducible characters of G. Character codegrees of finite groups have been intensely studied in the last decade. Various researchers have studied the influence of $\cod(G)$ on the structure of the group G. In this talk, we shall discuss the results on the character codegree of finite p-groups. 

4. Rijubrata Kundu, BITS Pilani 

Title: A relationship between character values of symmetric groups and wreath products

Abstract

5. Pralay Chatterjee, The Institute of Mathematical Sciences

Title:  Lower dimensional Betti numbers of a homogeneous space of a Lie group 

Abstract:  I will report on my work in collaboration with I. Biswas and C. Maity. We will give computable descriptions of the first four Betti numbers of a homogeneous space of a Lie group. We will also indicate how an interesting topological invariant is obtained using certain Lie theoretic data associated to a homogeneous space. We will apply the results when the homogeneous spaces are nilpotent orbits in a semisimple Lie group.

6. Sumit Kumar Upadhyay, IIIT Allahabad

Title: Multiplicative Lie algebra structures on a group

Abstract: In this talk, we will discuss some results related to the number of multiplicative Lie algebra structures (up to isomorphism) on a group.

7. Sushil Bhunia, BITS Pilani, Hyderabad

Title: Reality in rank-one Lie groups

Abstract

8. Ram Karan Choudhary, IISER Pune

Title: The Waring problem for matrices over finite local rings 

Abstract:  The classical Waring problem asks whether every natural number can be expressed as a bounded sum of k-th powers. The problem was answered affirmatively by Hilbert in 1909, and it has since inspired analogous questions for various algebraic structures, including groups, rings, algebras, and Lie algebras. In 2025, Krishna Kishore and Anupam Singh proved that, for sufficiently large q, every matrix over F_q can be expressed as a sum of two k-th powers [Kishore and Singh, Israel J. Math. 267 (2025), 301–320]. This motivates the corresponding problem over finite local rings. Let O_ℓ  be a finite principal local ring with residue field F_q, and let k be a positive integer. We ask whether every matrix over O_ℓ  can be expressed as a sum of two k-th powers. We prove that, if minus one is a k-th power in F_q and the characteristic of F_q does not divide k, then, for sufficiently large q, every matrix over O_ℓ  can be expressed as a sum of two k-th powers. We also show that both conditions are necessary in general. This talk is based on a joint work with Harish Kishnani and Anupam Singh.

9. Dibyendu Das, ISI Bangalore

Title: Solvability of automorphism groups of commutative algebras and isolated hypersurface singularities

Abstract

10. Sayan Pal, ISI Bangalore

Title: Orbit spaces in some PV's associated to Sp_6

Abstract: In this talk, we will discuss the orbit space decompositions in some prehomogeneous vector spaces (in short PV) associated to the group Sp_6. These are representations of algebraic groups with a phenomenon of classifying several algebraic structures in terms of their orbit spaces. In our earlier work, we got a parametrization of the composition algebras defined over a field k in terms of the orbit spaces in some of these representations. Here we will see that we can also trace the containments of these composition algebras as subalgebras inside the other composition algebras using the orbit space decompositions of the semi-stable sets in some PVs. 

11. Maneesh Thakur, ISI Bangalore

Title:  Automorphism groups of some geometries associated with composition algebras

Abstract:  We will describe some projective geometries associated to composition algebras and discuss their automorphism groups. If time permits, mention some results recently obtained.

12. Dilpreet Kaur, IIT Jodhpur

Title: Hayashi property for conjugation quandles

Abstract: We call a permutation σ ∈ S_n a regular permutation if its disjoint cycle decomposition contains a cycle with length equal to the order o(σ). Hayashi conjectured that all right translation maps of a connected quandle are regular permutations.  The property of this conjecture is generalized for all finite quandles by the name of the Hayashi property. In this talk, we first discuss the group-theoretic equivalence of the Hayashi property for conjugation quandles, and use this to study the Hayashi property of conjugation quandles defined on finite irreducible Coxeter groups. 

13. Varadharaj R. Srinivasan, IISER Mohali

Title: A Study of algebraic differential equations via algebraic groups

Abstract

14. Pradeep Kumar Rai, Mahindra University Hyderabad 

Title: Bogomolov multiplier and $\Sha$-rigidity of finite groups 

Abstract: The Bogomolov multiplier of a finite group is defined as the subgroup of the second cohomology group with coefficients in $C^*$ consisting of those cohomology classes which vanish after restriction to all abelian subgroups of the group. It represents an obstruction to the Noether's problem on rationality of fixed fields. In this talk we shall address a question of Boris Kunyavski regarding a connection between the Bogomolov multiplier and $\Sha-rigidity (in the sense that all their class-preserving automorphisms are inner) of a group. Then we shall present a work of ours where we have shown the existence of a group G with trivial Bogomolov multiplier such that the Bogomolov multiplier of a central product G*G is non-trivial.

15. B. Sury, ISI Bangalore and ICTS-TIFR 

Title: Algebraic groups with good reduction and applications

Abstract:  In the last 5 or 6 years, surprising and exciting connections between the study of algebraic groups with good reduction and the genus problem, which is concerned with characterizing simple algebraic groups in terms of their maximal tori over the field of definition, have emerged. The developments and conjectures provide a pathway towards the study of linear algebraic groups over higher-dimensional fields. We will provide an overview of this topic.

16. Amit Kulshrestha, IISER Mohali 

Title: 

Abstract:

17. Prachi Saini, IISER Mohali

Title: Noncommutative polynomials and their images on algebras

Abstract: The study of polynomial identities has played an important role in understanding the structure of noncommutative algebras. A related, and often more subtle, problem is to determine the set of values attained by a polynomial when evaluated on an algebra. One may ask, for example, whether the image has some linear structure, which subspaces can occur as images, and under what conditions the associated polynomial map is surjective. A prominent problem in this direction is the L’vov-Kaplansky conjecture, which predicts that the image of a multilinear polynomial on a matrix algebra is a vector space. In this talk, I will discuss image problems for noncommutative polynomial maps and their variants, particularly when coefficients from the underlying algebra are allowed. I will focus on questions concerning the structure and size of polynomial images, surjectivity, and related Waring-type problems.

18. Sumit Chandra Mishra, IIT Indore

Title: Ruled residue theorem for function fields in one variable 

Abstract:  Let E be a field with a valuation v. In 1983, Ohm proved that for any extension of v to the rational function field E(X)  in one variable, the corresponding residue field extension is either algebraic or ruled, i.e., it is the rational function field in one variable over a finite extension of the residue field of E. This is called the Ruled Residue Theorem. More generally, one can ask if such a statement holds for the function field F of a curve over E? If not, is there any bound on the number of extensions of v to F where this fails? I will mention known results for the function fields of conics. Later on, I will discuss the case of function fields of elliptic curves (joint work with Becher & Gupta (2024)) and function fields of hyperelliptic curves (joint work with Gupta (2026)).

19. Siddhartha Sarkar, IISER Bhopal

Title: Uni-width subgroups, universal elements, and lambda number of finite groups

Abstract:  A cyclic subgroup N of a finite group G is called a uni-width subgroup of G if N is the unique cyclic subgroup of G of order |N|. In fact, a finite group G admits a unique largest uni-width subgroup denoted by U(1; G). We will then show how the prime factors of the order of U(1; G) influence the structure decomposition of the Fitting subgroup Fit(G) of G. As an application, we will show that the structure of U(1; G) influences the power graph coloring invariant, namely $\lambda(G)$, and the universal element of the power graph of G. If time permits, we will also introduce the concept of d-width subgroups in general. There are similar structural results for the 2-width (or twin-width subgroups) of a finite group G. This latter part is a joint work with Rahul Kitture.

20. Arijit Mahato, NISER Bhubaneswar

Title: Automorphisms of star-shaped Coxeter groups

Abstract: In this talk, we discuss the automorphisms of Coxeter groups, with particular emphasis on those admitting a finite star-shaped Coxeter diagram. We show that the automorphisms of each such Coxeter group can be described in terms of inner automorphisms, diagram automorphisms, and three additional nontrivial classes of automorphisms arising from the reflections and parabolic subgroups. Furthermore, we provide structural descriptions of these automorphism groups and analyse the role of each class of automorphisms in determining the overall structure of the automorphism group.

Poster Presentation:

1. Khyati Sharma, IISER Berhampur

2. Sahanawaj Sabnam , NISER Bhubaneswar

3. Shilpa Rani, SRM, AP

4. Sutirtha Datta, IISER Pune

5. Harish Kishnani, IISER Pune

6. Ayon Roy, IISER Pune

7. Ritika Choudhary, Thapar Institute of Engineering and Technology, Patiala

Participants:

1. Rahul Kaushik, IIIT Pune

2. Ayon Roy, IISER Pune

3. Harish Kishnani, IISER Pune

4. Ram Karan Choudhary, IISER Pune

5. Ahona Mukherjee, IISER Pune

6. Avik De, ISI Bangalore

7. Sahanawaj Sabnam, NISER Bhubaneswar.

8. Ritika Choudhary, Thapar Institute of Engineering and Technology, Patiala.

9. Shilpa Rani, SRM University, AP

10. Khyati Sharma, IISER Berhampur

11. Pratham Roy, IISER Pune

12. Antara Manik, IISER Pune

13. Haritha, IISER Pune

14. Divyasree, IISER Pune

15. Rishabh Jain, IISER Pune

16. Aniket Sen, IISER Pune

17. Akshay Kharade, IISER Pune 

18. Umasankar Khatua, IISER Pune 

19. Debajyoti Deb, IISER Pune

20. Aniruddha Maji, IISER Pune

21. AbirRangan Datta, IISER Pune

22. Sandip Mandal, IISER Pune

23. Nipurn Shakya, IISER Pune 

24. Subhash Ranjan Choudhary, IISER Pune  

25. Kavinesh R, IISER Pune 

26. Sutirth Datta, IISER Pune

27. Dhrubajyoti Das, IISER Pune

28. Antik Paul, IISER Pune

29. Anuj Kumar Bhagat , IISER Pune

30. Revati Shivanand Divekar, IISER Bhopal

31. Aman Ali Malitya, IISER Pune

32. Arup Mondal , IISER Pune

33. Gaurav Kumar, IISER Pune

34. Pratham A. Johari, IISER Pune