# Alexandros Groutides

I am a second year PhD student working in Algebraic Number Theory, under the supervision of Professor David Loeffler. I am currently working on integral structures in smooth representations of $p$-adic groups, zeta integrals, and their applications to Euler systems and automorphic forms.

**Education:**

I completed my MSc at the University of Oxford where I wrote my thesis on $\ell$-adic and adelic Galois representations attached to elliptic curves and Serre's open image theorems, under the supervision of Dr James Newton. A copy of my masters thesis is available hereLink opens in a new window. Before that I completed my BSc at University College London. My CV can be found hereLink opens in a new window

**Research:**

- On Rankin-Selberg integral structures and Euler systems for $\mathrm{GL}_2\times \mathrm{GL}_2$. (July 2024) [arxiv].
- Integral structures in smooth $\mathrm{GL}_2(\mathbf{Q}_p)$-representations and zeta integrals. (Jan 2024) [arxiv]. Submitted.

**Talks:**

- YRANT-VI - University of Oxford (July 2024): When Rankin-Selberg periods meet Euler systems.
- University of Warwick junior number theory seminar (June 2024): Integral structures in spherical GL(2)-representations distinguished by an unramified maximal torus.
- University of Sheffield number theory seminar (February 2024): On integral structures in smooth $\mathrm{GL}_2$-representations and zeta integrals.
- Junior London number theory seminar, LSGNT (February 2024): Integral structures in smooth $\mathrm{GL}_2(\mathbf{Q}_p)$-representations.
- Tate's thesis reading group, University of Warwick (June 2023): Analytic class number formula via adeles.
- Tate's thesis reading group, University of Warwick (June 2023): Local and global zeta integrals and functional equations.
- Introduction to $p$-adic geometry, University of Warwick (April 2023): Perfectoid Shimura curves.
- Modular forms, University of Warwick (April 2023): Eichler-Shimura isomorphism with twisted coefficients in cohomology.
- Eigenvariety reading group, University of Warwick (January 2023): Functional analysis over non-Archimedean complete valued fields.
- Postgraduate seminar, University of Warwick (November 2022): -adic and adelic Galois representations attached to elliptic curves and Serre’s open image theorems.
- Elliptic curve isogeny based cryptography reading group, University of Warwick (October 2022): Elliptic curves over finite fields and Velu’s formulae.

**Conference travel****:**

- ENTR Workshop - Universität Duisburg-Essen (September 2024)
- Representations of $p$-adic groups and the Langlands Correspondance, in honor of Colin Bushnell - King's College London (September 2024)
- YRANT - VI - University of Oxford (July 2024)
- Modular Forms, L-functions, and Eigenvarieties in memoriam of Joël Bellaïche - École Normale Supérieure (June 2024)
- Arithmetica Transalpina - UniDistance Suisse (May 2024)
- YRANT - V - University of Cambridge (September 2023)

- New perspectives in pure mathematics - University of Bristol (March 2023)

**Teaching:**

- Teaching assistant for MA267 Groups and Rings (2023-2024)

**Miscellaneous:**

- Personalized complete set of lectures notes based on Miles Reid’s Commutative Algebra II course at the university of Warwick: Commutative Algebra II
- Equivalence
*here.*

**Contact:**

alexandros.groutides@warwick.ac.uk