{"id":38,"date":"2023-11-06T17:07:23","date_gmt":"2023-11-06T17:07:23","guid":{"rendered":"https:\/\/hodge.maths.ed.ac.uk\/?page_id=38"},"modified":"2026-10-26T23:32:55","modified_gmt":"2026-10-26T23:32:55","slug":"hodge-club","status":"publish","type":"page","link":"https:\/\/hodge.maths.ed.ac.uk\/?page_id=38","title":{"rendered":"Hodge Club"},"content":{"rendered":"\n
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The Hodge Club is the seminar for Hodge Institute graduate students and postdocs. That means we’re interested in Algebra, Geometry, Topology, Number Theory, and all possible combinations and derivations of the four. Before the 2016\/17 academic year, the Hodge Club was known as the Geometry Club.<\/p>\n\n\n\n

We meet every Friday at 16:30<\/strong>, where we take it in turns to present a topic of interest to the rest of the group. We hope to run this as a hybrid seminar<\/strong>, so in particular we will have both an in person and virtual audience. If you are attending in person, we will normally meet at Bayes 5.46<\/strong> (exceptions announced by e-mail). If you are attending virtually, you can join using this <\/strong>Teams link<\/a>. If you do not receive the weekly emails and would like to be added to the mailing list, please get in touch with one of the organisers.<\/p>\n\n\n\n

Talks tend to be fairly informal and provide excellent practice for conference talks in front of a friendly audience. You can find our current schedule and a historical list of talks below.<\/p>\n\n\n\n

The Hodge Club for the 2026\/27 academic year is organised by Cassia Edwards<\/a><\/strong>, Mia Lam<\/a><\/strong>, and Sruthy Joseph<\/strong>.<\/p>\n<\/div>\n<\/div>\n\n\n\n

Here is the link for the last years’ talks: https:\/\/hodge.maths.ed.ac.uk\/?page_id=1073<\/a>.<\/p>\n\n\n\n

Current Schedule of talks for 2026\/27<\/p>\n\n\n\n

9th October<\/strong> | Isky Mathews (Edinburgh) | Electrodynamics at Lightspeed
Note: This session took place at 4pm at Heriot-Watt University<\/em><\/p>\n\n\n\n

In this talk, I hope to convey something of the subject of classical electrodynamics and how exciting it can be. With just a little calculus, Maxwell was able to explain so many puzzling phenomena which had come before him, unifying the behaviour of currents and magnets and as an unexpected byproduct also light! We will rather ambitiously attempt to take the viewer from not knowing anything to why the sky is blue in just this talk, so get ready for a (highly non-rigorous) ride!<\/p>\n\n\n\n

16th October<\/strong> | Violeta L\u00f3pez (St Andrews) | A new Brill\u2013Noether general tropical curve<\/p>\n\n\n\n

Divisors on a \u2018general\u2019 algebraic curve are well understood: the Brill\u2013Noether theorem tells us that they have the expected rank. Considering degenerations of algebraic curves we get tropical curves, however, the Brill\u2013Noether theory of tropical curves is not entirely understood. In this talk we will focus on tropical curves with a divisorial behaviour similar to the one of general algebraic curves. These are called Brill\u2013Noether general and we will introduce a new family of such curves, known as chains of theta-graphs and loops.<\/p>\n\n\n\n

23rd October<\/strong> | Alistair Severn (Glasgow) | Counting problems in Arithmetic Geometry<\/p>\n\n\n\n

The three classical questions in Arithmetic Geometry are:<\/p>\n\n\n\n

    \n
  1. Given a variety, does it have a rational point?<\/li>\n\n\n\n
  2. Given a variety with at least one rational point, are there infinitely many rational points?<\/li>\n\n\n\n
  3. Given a variety with infinitely many rational points, what is their asymptotic distribution?<\/li>\n<\/ol>\n\n\n\n

    In this talk we discuss two conjectures – both saying something quantitative about the behaviour of rational points on algebraic varieties. Manin’s conjecture proposes an answer to question 3, whilst the Loughran\u2014Smeets conjecture proposes an answer to question 1 “on average”. A central motto in this area is that geometry should determine arithmetic, so we shall spend some time discussing the input from Algebraic Geometry, before talking briefly about some recent results on counting the number of soluble fibres in conic bundles due to Destagnol–Lyczak–Sofos (2025) and myself (2026).<\/p>\n\n\n\n

    30th October<\/strong> | Sruthy Joseph (Edinburgh) | Condensed abelian groups<\/p>\n\n\n\n

    How to do homological algebra when the algebraic objects carry a topology? For example, we cannot do homological algebra in the category of topological abelian groups since it is not an abelian category. This problem was addressed by defining a larger category, called the category of condensed abelian groups, which forms a Grothendieck abelian category. In the talk, we will define condensed abelian groups and discuss some key properties of the category of condensed abelian groups. If time permits, we will also see a candidate for the Pontryagin dual of a condensed abelian group that satisfies the duality at the level of locally compact abelian groups, and demonstrate why this choice of dual does not satisfy Pontryagin duality in the category of condensed abelian groups.<\/p>\n\n\n\n

    6th November<\/strong> | Social<\/p>\n\n\n\n

    13th November<\/strong> | Raisa Serova (Edinburgh) | TBC<\/p>\n\n\n\n

    TBC<\/p>\n\n\n\n

    19th November<\/strong> | Maria De Leyva Elola-Olaso (Barcelona) | TBC
    Note: This session has been moved one day back to Thursday<\/em><\/p>\n\n\n\n

    TBC<\/p>\n\n\n\n

    27th November<\/strong> | Alex Zahrer (TalTech) | TBC<\/p>\n\n\n\n

    TBC<\/p>\n\n\n\n

    4th December<\/strong> | Jo\u00e3o Camarneiro (Edinburgh) | TBC<\/p>\n\n\n\n

    TBC<\/p>\n\n\n\n

    11th December<\/strong> | Ilias Papadimitriou (HWU) | TBC<\/p>\n\n\n\n

    TBC<\/p>\n","protected":false},"excerpt":{"rendered":"

    The Hodge Club is the seminar for Hodge Institute graduate students and postdocs. That means we’re interested in Algebra, Geometry, Topology, Number Theory, and all possible combinations and derivations of the four. Before the 2016\/17 academic year, the Hodge Club was known as the Geometry Club. We meet every Friday at 16:30, where we take it […]<\/p>\n","protected":false},"author":1,"featured_media":76,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-38","page","type-page","status-publish","has-post-thumbnail","hentry"],"_links":{"self":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages\/38","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=38"}],"version-history":[{"count":119,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages\/38\/revisions"}],"predecessor-version":[{"id":1103,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/pages\/38\/revisions\/1103"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=\/wp\/v2\/media\/76"}],"wp:attachment":[{"href":"https:\/\/hodge.maths.ed.ac.uk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=38"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}