Schedule: 1, 2, 3, 4 June 2021 (1400 - 18:30 hours Indian Standard Time) each day up to 6 talks of half an hour duration with virtual tea breaks.
Group Theory Sangam Conference -Schedule/timetable
Keeping in mind a large number of registration and bandwidth issue, all lectures will be also telecast live on YouTube at the following links:
Day 01 (1 June 2021): https://www.youtube.com/watch?v=eeKsDLaLPxY
Day 02 (2 June 2021): https://www.youtube.com/watch?v=LLJn2AGLlc4
Day 03 (3 June 2021): https://www.youtube.com/watch?v=RHCM-6EO5_Q
Day 04 (4 June 2021): https://www.youtube.com/watch?v=EOADfmPjRQE
Daily timetable:
Talk 1: 14:00-14:30 (IST)
Talk 2: 14:30-15:00 (IST)
Talk 3: 15:00-15:30 (IST)
Break
Talk 4: 16:00-16:30 (IST)
Talk 5: 16:30-17:00 (IST)
Talk 6: 17:00-17:30 (IST)
01 June 2021
(Incharge: Viji Thomas, Amit Kulshrestha)
Subhrajyoti Saha, Monash University, Australia
Title: Skeleton groups and their isomorphism problem
Walaa Nabil Taha Fasfous , Tezpur University
Title : Various spectra and energies of commuting and non-commuting graphs of finite groups.
Mani Shankar Pandey, Indian Institute of Information Technology, Allahabad
Title: Notion of commutators in a multiplicative Lie algebra.
Dávid R. Szabó, Affiliations: (1) Alfréd Rényi Institute of Mathematics, Budapest, Hungary, (2) Department of Mathematics, Central European University
Title: Class 2 finite nilpotent groups, Heisenberg groups and applications
Egor Voronetsky, Department of Mathematics and Mechanics, St Petersburg University, Russia.
Title: An explicit presentation of relative Steinberg groups
Tejbir Lohan, IISER Mohali.
Title: Reversibility of hermitian isometries.
02 June 2021
(Incharge: Amit Kulshrestha, Anupam Singh, Shripad Garge)
Sridhar P. Narayanan, Institute of Mathematical Sciences
Title: Some results on the restriction problem
Abstract: Let $\lambda$ be a partition with at most $n$ parts and let $W_\lambda(C^n)$ denote the irreducible representation of $GL_n$ corresponding to $\lambda$. Let $\mu$ be a partition of $n$ and let $V_\mu$ denote the irreducible representation of $S_n$ corresponding to $\mu$. Identifying $S_n$ with the subgroup of permutation matrices in $GL_n$, we may define the restriction coefficient $r_{\lambda \mu}$ to be the multiplicity of $V_\mu$ in the restriction of $W_\lambda$ to $S_n$.
The restriction problem aims to find a combinatorial interpretation for the coefficients $r_{\lambda \mu}$. The problem has long remained open, but is known to be connected to the expansion of plethysms of symmetric functions. Recent renewed attention in this problem has followed the work of R. Orellana, M. Zabrocki, S. Assaf, D. Speyer, etc.
We offer solutions to the restriction problem in a few cases, and a sketch of the simple proof that obtains these results.
Sumana Hatui, Department of Mathematics at Indian Institute of Science, Bangalore
Title: On monomial and finite dimensional projective representations of groups
Abstract: The study of projective representations of a group has a long history starting from the work of Schur. In this talk, we describe the Schur multiplier and representation group of discrete Heisenberg groups. Then we give a characterization of monomial projective representations of finitely generated nilpotent groups and a characterization of polycyclic groups whose projective representations are finite dimensional. This talk is based on the joint work with Pooja Singla and E.K. Narayanan.
Neha Malik, IISER Pune
Title: The Total Stiefel-Whitney Class of a Orthogonal Representation of SL(n, q)
Matteo Pintonello, University of the Basque Country in Spain.
Title: On the generation of verbal subgroups in profinite groups.
John McHugh, University of California in Santa Cruz
Title: On the image of the trivial source ring in the ring of virtual characters of a finite group
Abstract: Let G be a finite group and let O be a complete discrete valuation ring whose residue field is algebraically closed of positive characteristic p. The character of a finitely generated O-free OG-module can be considered as an element of R(G), the virtual character ring of G. In particular, "taking characters" gives a map from the ring T_{O}(G) of trivial source OG-modules to R(G). By a theorem of A. Dress, the image of this map is a subring of the ring of p-rational characters. We give a "detection theorem'' that answers the question: when is a p-rational character of G contained in the image of T_{O}(G)? It turns out that when p is odd every p-rational character is contained in the image. This is not the case when p=2: the quaternion group Q_8 is a counterexample. We show that, in the p=2 case, any other counterexample "comes from" Q_8. The theories of biset functors (introduced by S. Bouc) and fibered biset functors (developed by R. Boltje and O. Coşkun) make this precise.
03 June 2021
(Incharge: Shripad M. Garge, Amit Kulshrestha)
Sushil Bhunia, IISER Mohali
Title : Twisted Conjugacy in Big Mapping Class Groups.
Abstract: Let φ be an automorphism of a group G. Two elements x and y of G are said to be φ-twisted conjugate if gx =yφ(g) for some g in G. This is an equivalence relation on G, and the equivalence classes are called th e φ-twisted conjugacy classes or the Reidemeister classes of φ. If φ = Id, then the φ-twisted conjugacy classes are the usual conjugacy classes. A group G is said to have the R_{∞} -property if the number of its φ-twisted conjugacy classes is infinite for every automorphism φ of G. In this talk I will describe when a big mapping class group (i.e., mapping class group of an infinite type surface) possesses the R_{∞} -property. This is a work in progress with Swathi Krishna.
M. M. Radhika, TIFR Mumbai
Title: On the congruence subgroup problem
Arunava Mandal, Indian Statistical Institute, Bangalore
Title: The structure of Cartan subgroups in Lie groups.
Abstract: Cartan subgroup is a classical object in the structure theory of Lie groups. This was defined by Chevalley in 1955. It was extensively studied by Borel, Chevalley, Goto, Wustner, and many others. In this talk, we will discuss recent developments on this topic. (This is joint work with Riddhi Shah, to appear in Math. Zeit.)
Tushar Kanta Naik, IISER Mohali, Mohali
Title: Automorphisms of (Odd) Coxeter groups (A study motivated by Artin braid groups and twin groups).
Alexander Trost, Ruhr University Bochum, Germany.
Title : Strong boundedness of arithmetic Chevalley groups-A short overview.
Ashish Mishra, Federal University of Pará, Belém, Brazil
Title: A sangam of spectral approach and Schur–Weyl duality
04 June 2021
(Incharge: Gurmeet Bakshi, Manoj Kumar, Amit Kulshrestha)
Sumit Chandra Mishra, IIT Bombay
Title: Local-global principles for norms and multinorms over semi-global fields
Gurleen Kaur, Department of Mathematical Sciences, IISER Mohali
Title: The algebraic structure of rational group algebras: From classical to modern approach.
Komma Patali, IISER TVM.
Title: A property of p-groups of nilpotency class p + 1.
Abstract: In a p-group G of nilpotency class p + 1, we prove that the exponent of the commutator subgroup divides the exponent of G/Z(G). As a consequence, we prove that the exponent of the second homology group H2(G, Z) divides exp(G), in a finite p-group G of class p. This is joint work with A.E. Antony, and V.Z. Thomas.
Ratan Lal, Central University Of Rajasthan
Title: Classifying gyrotransversals in groups
Abstract: In this paper, we classify the gyrotransversals up to isomorphism in a group G to a fixed subgroup of it. As an application, we have calculated the isomorphism class of gyrotransversals in finite dihedral group to any subgroup of it. As a consequence, we get a lower bound for non-isomorphic right gyrogroups of order n.
Abhay Soman, University of Hyderabad
Title: On triviality of the reduced Whitehead group over Henselian fields.
Carmine Monetta, University of Salerno (Italy)
Title: On a construction related to the non-abelian tensor square of groups
Scientific Organising Committee:
Anupam Kumar Singh, IISER Pune, India
Manoj Kumar Yadav, HRI Pryagraj, India
Shripad M. Garge, IIT Bombay, Mumbai, India
Amit Kulshrestha, IISER Mohali, India
Gurmeet Bakshi, Panjab University, Chandigarh, India
Viji Thomas, IISER Thiruvananthapuram, India
Where: Online over zoom. Please write at grouptheory21@gmail.com for free registration.
Who can give a talk: This conference is aimed to promote research work done by younger colleagues working in the subject of Group Theory. We aim to have senior PhD students, Post-docs and young faculty (including the ones who are young at heart) present their work from across the globe.
Duration of talks: The duration of each talk will be 25 minutes + 5 minutes for Q&A. (The speakers will be advised to prepare a slide presentation to avoid technical difficulties).
What to do if you are interested in giving a talk: If you are interested in giving a talk, please send the following details by email at grouptheory21@gmail.com before 30 April 2021. APPLICATION IS CLOSED NOW
Your Name
Affiliation
Present position (PhD student, Post-doc, faculty)
The title of the proposed talk together with extended abstract (roughly a page long).
The scientific organising committee will look at the extended abstracts received and will announce the candidates to give talks by 15 May 2021.