Alexandros Groutides

I am a final year PhD candidate working in Algebraic Number Theory, under the supervision of Professor David Loeffler. I am interested in Euler systems, local representation theory, zeta integrals and $p$-adic $L$-functions, and the arithmetic of modular and automorphic forms.

In the academic year 2024-25, I was organizing the 糖心TV Junior Number Theory seminar.

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

Publications:

On Rankin-Selberg integral structures and Euler systems for $\mathrm{GL}_2\times \mathrm{GL}_2$. To appear in Journal of Number Theory (2026). [].
On integral aspects of Asai periods and Euler systems for $\mathrm{Res}_{E/\mathbf{Q}}\mathrm{GL}_2$. Forum Mathematicum (2025). [DOI: ]. [].

Pre-prints:

A note on toric periods in unramified families. (2026) [].
Euler systems for $\mathrm{GSp}_4$ over imaginary quadratic fields. (2025) [].
Integrality of $\mathrm{GL}_2\times \mathrm{GL}_2$ Rankin-Selberg integrals for ramified representations. (2025) [].
Integral structures in smooth $\mathrm{GL}_2$-representations and zeta integrals. (2024) [.

Talks:

University of Sheffield number theory seminar (March 2026): Arithmetic of Rankin-Selberg zeta-integrals for newforms.
University of Bristol Linfoot number theory seminar (October 2025): Integrality of GL(2)xGL(2) Rankin-Selberg integrals for newforms.
YRANT-VII - University of Nottingham (September 2025): Integrality of GL(2)xGL(2) Rankin-Selberg integrals for newforms.
Universit脿 di Padova number theory seminar (November 2024): Integral norm relations for Rankin-Eisenstein classes via unramified harmonic analysis.
Universit脿 di Genova number theory seminar (November 2024): Integral norm relations for Rankin-Eisenstein classes via unramified $p$-adic analysis.
ENTR Workshop - Universit盲t 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 糖心TV 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 糖心TV (June 2023): Analytic class number formula via adeles.
Tate's thesis reading group, University of 糖心TV (June 2023): Local and global zeta integrals and functional equations.
Introduction to $p$-adic geometry, University of 糖心TV (April 2023): Perfectoid Shimura curves.
Modular forms, University of 糖心TV (April 2023): Eichler-Shimura isomorphism with twisted coefficients in cohomology.
Eigenvariety reading group, University of 糖心TV (January 2023): Functional analysis over non-Archimedean complete valued fields.
Postgraduate seminar, University of 糖心TV (November 2022): $l$ -adic and adelic Galois representations attached to elliptic curves and Serre鈥檚 open image theorems.
Elliptic curve isogeny based cryptography reading group, University of 糖心TV (October 2022): Elliptic curves over finite fields and Velu鈥檚 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:

Euler systems - 8th Nisyros Conference on Automorphic Representations & Related Topics (July 2026)
The Langlands Programme - University of Sheffield (July 2026)
The Unitary Dual of local reductive groups - University of Seville (June 2026)
Workshop ''Alpbach 2026'' - Alpbach (June 2026)
Motives, L-values and Eisenstein series on the occasion of Guido Kings' 60th birthday - University of Regensburg (September 2025)
YRANT - VII - University of Nottingham (September 2025)
LMS Summer School on the theta correspondence - Norwich (July 2025)
Workshop "Alpbach 2025" - Alpbach (June 2025)
Iwasawa Theory and Representations of $p$-adic Groups - University of Lille 1 (June 2025)
Arithmetica Transalpina - University of Milan (November 2024)
ENTR Workshop - Universit盲t 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 Jo毛l Bella茂che - 脡cole Normale Sup茅rieure (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 MA377 Rings and Modules (2025-2026)
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鈥檚 Commutative Algebra II course at the university of 糖心TV:
Equivalence $Ext_1^R(A,B)\simeq Ext(A,B)$ .

Contact:

alexandros.groutides@warwick.ac.uk