Simons Dissertation Fellowship<\/a> with previous applicants and awardee.<\/p>\n\n\n\n
\n\n\n\n02\/13\/2026 – Mattie Ji: Teaching Algebraic Topology Using Electrical Circuits<\/h2>\n\n\n\n
Abstract:<\/strong> In this talk, I will describe a perspective, originally due to Weyl in 1923, that fundamental concepts in electrical circuits can be naturally interpreted as statements about homology and cohomology of graphs. Thus, one can motivate and introduce the theory of (co)homologies using electrical circuits, which is the approach this talk would take. No prior knowledge of electrical circuits or (co)homologies are necessary. If time permits, I may try to sketch some work I have on what are called “brave new \/ homotopical electrical circuits”, which I plan to post on April 1st, 2026.<\/p>\n\n\n\n
\n\n\n\n02\/20\/2026 – Katie Ellman-Aspnes: Classification Theory and the Map of the Universe<\/h2>\n\n\n\n
Abstract:<\/strong> Model theory enables us to analyze the complexity of various mathematical objects that are structurally very different, such as a graph with a group or a field with a topological space. In this talk we’ll discuss what it means for a mathematical object to be classifiable and some indicators of complexity that show when an object is not classifiable. We’ll also take a look at the model-theoretic “map of the universe,” which is a means of visually organizing various types of mathematical objects according to model-theoretic degrees of complexity.<\/p>\n\n\n\n
\n\n\n\n02\/27\/2026 – Cory Gillette: A Friendly Introduction to Monads<\/h2>\n\n\n\n
Abstract: <\/strong>Monads are one way of making formal sense of what we mean when we speak about sets “equipped with some structure”. We will try to give enough examples to convince you that these occur frequently in nature. We will also discuss some theorems and applications. We will not assume familiarity with category theory.<\/p>\n\n\n\n
\n\n\n\n03\/06\/2026 – Joshua Lehman: The Degree-Genus Formula<\/h2>\n\n\n\n
Abstract:<\/strong> Algebraic curves in the complex projective plane are, topologically, two dimensional surfaces. I’ll give three different ways of computing their genus and draw pictures of (nice) curves (don’t worry, drawing a squiggly line doesn’t count!).<\/p>\n\n\n\n
\n\n\n\n03\/13\/2026 – SPRING BREAK: NO TALK<\/strong><\/h2>\n\n\n\n
\n\n\n\n03\/20\/2026 – Academic jobs panel<\/h2>\n\n\n\n
Abstract<\/strong>: We are very lucky to have Annie Holden, Jui-Yun Hung, Katherine Novey (all current ND grad students), and Lorenzo Riva (a previous ND grad student) who will talk to us about their experiences of academic job applications and try to answer any questions we may have.<\/p>\n\n\n\n
\n\n\n\n03\/27\/2026 – Chen-Kuan Lee: Riemannian Holonomy and Berger’s List<\/h2>\n\n\n\n
Abstract:<\/strong> Riemannian geometry is a branch of differential geometry that studies manifolds equipped with a Riemannian metric, which provides a way to measure distances and angles. In this talk, we will introduce the concept of holonomy groups, with a focus on Riemannian holonomy. We will then discuss how holonomy interacts with the topology of manifolds by highlighting Berger\u2019s classification of possible Riemannian holonomy groups.<\/p>\n\n\n\n
\n\n\n\n04\/03\/2026 – EASTER BREAK: NO TALK<\/h2>\n\n\n\n
\n\n\n\n04\/10\/2026 – Tan \u00d6zalp: A Hat Problem<\/h2>\n\n\n\n
Abstract<\/strong>: We describe a game of prisoners and hats and construct a non-measurable function.<\/p>\n\n\n\n
\n\n\n\n04\/17\/2026 – NO TALK<\/h2>\n\n\n\n
\n\n\n\n04\/24\/2026 – Jenny Xu: Compact Right Topological Semigroups and their Idempotents<\/h2>\n\n\n\n
Abstract:<\/strong> I will talk about compact right topological semigroups, their idempotents, and maybe Hindman’s theorem.<\/p>\n\n\n\n
\n\n\n\n05\/01\/2025 – Luis Atzin Franco-Reyna: (Not WIRED) 4 Levels of Calculus of Variations in Geometry<\/h2>\n\n\n\n
Abstract:<\/strong> One of the most elegant ideas in math is the idea of optimization of a function. The tools of carrying out this procedure are manifold (pun intended), one of which is the calculus of variation. Mimicking the famous WIRED 5 level series, I will attempt to explain this idea in 4 levels that (hopefully) is easily understandable.
<\/p>\n\n\n\n<\/p>\n","protected":false},"excerpt":{"rendered":"
01\/23\/2026 – Chase Bender: Rational Surfaces: Example One in Birational Geometry Abstract: Birational geometry is a subfield of algebraic geometry which has flourished in recent history\u2014especially in dimensions 3 and above\u2014due to the foundation laid by Grothendieck\u2019s scheme theory. Much of this progress is mo- tivated by the more classically understood theory of complex projective […]<\/p>\n","protected":false},"author":5114,"featured_media":0,"parent":55,"menu_order":-1,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1102","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages\/1102","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/users\/5114"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/comments?post=1102"}],"version-history":[{"count":17,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages\/1102\/revisions"}],"predecessor-version":[{"id":1217,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages\/1102\/revisions\/1217"}],"up":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages\/55"}],"wp:attachment":[{"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/media?parent=1102"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}