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Home  »  ARATHY VENUGOPAL

ARATHY VENUGOPAL

Academic Background

I obtained BSMS dual degree from IISER Tirupati in 2021, majoring in Mathematics. I joined my current PhD programme at IISER Tirupati in August 2022. I work under the guidance of Dr. Shalini Bhattacharya in Galois representations.

Arathy's Résumé

Research Interest

Our research interests primarily lie in the area of Galois representations.  It is useful to study the representations of absolute Galois group of Q  locally  by restricting it to  the decomposition subgroups at different primes p.  We are interested in research works related to the mod-p reductions of  2-dimensional local Galois representations attached to modular forms.  These representations are crystalline if the level of the modular form is prime to p. In this case, the results concerning  the structure of modular representations of the general linear group of degree 2 over a finite field plays an important role in the explicit computation of the reduction.

Advisor Information

Dr Shalini Bhattacharya is an Assistant Professor at School of Statistics and Mathematics, University of Hyderabad, who works in Algebraic Number theory. In particular, she is interested in the theory of Modular forms and Galois representations. Before joining University of Hyderabad, she was assistant professor at Dept. of Mathematics, IISER Tirupati. She obtained her doctoral degree from the Tata Institute of Fundamental Research (TIFR) Bombay, after which she worked as a post-doctoral researcher at Bar-Ilan University, Israel and then at Max-Planck Institute for Mathematics, Germany. Her research interests include studying mod-p reduction of certain crystalline representations using mod-p semi-simple local Langlands Correspondence.

Courses taken

I have taken 6 courses (24 credits) during my PhD course work.

  • MTH 611- Algebra I ( Fields and Galois theory)
  • MTH 612-  Analysis I (Functional Analysis)
  • MTH 613- Topology I (Algebraic Topology -I)
  • MTH 621- Algebra II  (Commutative Algebra)
  • MTH 623- Topology II (Algebraic topology – II)
  • MTH 624- Representation theory

Internal Teaching Assistantships

  • MTH 211 – Probability and Statistics
  • MTH 121 – Linear algebra and applications

External Teaching Assistantships:

      (Nov 2023- present) at S.V. Engineering college Tirupati

  • Vector differentiation, Vector integration and Vector operators
  • Linear Algebra and Calculus

Achievements:

  • Academic excellence award 2024, IISER Tirupati
  • Cleared CSIR-NET Lectureship October 2022
  • Received Provisional offer for INSPIRE fellowship 2021
  • Recipient of INSPIRE  SHE Scholarship (2016-2021)

Conferences/workshops attended:

  • Women in Numbers 2025 , hosted by IISER Pune ( January 2025)
  • Introduction to p-adic local Langlands program, NCMW, conducted at IIT Jammu ( September 2024)
  • New directions in Rational points , Chennai Mathematical Institute (January 2024)
  • Conference on Rational Points on Modular curves (September 2023)
  • Workshop on Elliptic Curves ( April 2023) conducted by National Centre for Mathematics at IISER Trivandrum.
  • Intercity Number theory Conference ( Feb 2023) hosted by Chennai Mathematical Institute.
  • Worked as Tutor for Annual Foundation School II ( May 2023) organised by National Centre for Mathematics.
  • Workshop on Group theory and Related Areas (Nov 2022) organized by IIIT Allahabad (Online)

Talks/presentations:

  • Poster presentation titled “On mod-p reduction of certain Crystalline representations” at PMRF Symposium 2025, held at IIT Hyderabad.