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Mathematics Institute

Alexandros Groutides

I am a third 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.

In the academic year 2024-25, I'm co-organizing the Warwick Junior Number Theory seminar. If you are interested in giving a talk please feel free to get in touch.

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 integral aspects of Asai periods and Euler systems for $\mathrm{Res}_{E/\mathbf{Q}}\mathrm{GL}_2$. (September 2024) [arxiv]. Submitted.
  • On Rankin-Selberg integral structures and Euler systems for $\mathrm{GL}_2\times \mathrm{GL}_2$. (July 2024) [arxiv]. Submitted.
  • Integral structures in smooth $\mathrm{GL}_2(\mathbf{Q}_p)$-representations and zeta integrals. (January 2024) [arxiv]. Submitted.

Talks:

  • Università di Padova number theory seminar (November 2024): Integral norm relations for Rankin-Eisenstein classes via unramified harmonic analysis.
  • Università di Genova number theory seminar (November 2024): Integral norm relations for Rankin-Eisenstein classes via unramified $p$-adic analysis.
  • ENTR Workshop - Universität Duisburg-Essen (September 2024): Rankin-Selberg integral structures and Euler systems for $\mathrm{GL}_{2} \times \mathrm{GL}_{2} $.
  • 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): l-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.

Posters:

  • Representations of $p$-adic groups and the Langlands Correspondance, in honor of Colin Bushnell - King's College London (September 2024): Integral aspects of Rankin-Selberg periods and applications.

Conference travel:

  • Arithmetica Transalpina - University of Milan (November 2024)
  • 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 MA3D5-15 Galois Theory (2024-2025)
  • 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 Ext_1^R(A,B)\simeq Ext(A,B) here.

Contact:

alexandros.groutides@warwick.ac.uk