Abstract:<\/strong> In this talk, we prove Monsky’s theorem, which states that it is impossible to dissect a square into an odd number of triangles of equal area. The only known proof of Monsky’s theorem uses the concept of valued fields and appears in Aigner and Ziegler’s book Proofs from THE BOOK<\/em>.<\/p>\n\n\n\n Abstract:<\/strong> The Hopf product conjecture is a classical open problem in differential geometry that asks whether the product of two 2-spheres admits a Riemannian metric with strictly positive curvature. In this talk, we will survey the history of the conjecture and discuss its significance in differential geometry.<\/p>\n\n\n\n Abstract:<\/strong> In the 1990s, D. Voiculescu developed the theory of free probability, a noncommutative analog of classical probability that proves to be useful in the study of operator algebras and random matrices. In this talk, I discuss motivations for this theory, some central concepts, and several important results related to this field of study.<\/p>\n\n\n\n Abstract:<\/strong> I will present a number of arguments against \u201csubstantial use\u201d of AI in mathematics (I will make precise what I mean by substantial use). The talk will have more-or-less two parts; in the first I will argue that substantial AI use is detrimental to the discipline of academic mathematics as a whole, and in the second I will argue that one is ill-served by substantial AI use at an individual level.<\/p>\n\n\n\n Abstract:<\/strong> TBA<\/p>\n\n\n\n Abstract:<\/strong> TBA<\/p>\n\n\n\n Abstract:<\/strong> TBA<\/p>\n\n\n\n Abstract<\/strong>: TBA<\/p>\n\n\n\n Abstract:<\/strong> TBA<\/p>\n\n\n\n Abstract: <\/strong>TBA<\/p>\n\n\n\n Abstract<\/strong>: TBA<\/p>\n\n\n\n Abstract: <\/strong>TBA<\/p>\n\n\n\n Abstract:<\/strong> TBA<\/p>\n\n\n\n Abstract:<\/strong> TBA<\/p>\n\n\n\n <\/p>\n","protected":false},"excerpt":{"rendered":" 08\/31\/2026 – Gavin Dooley: Monsky’s Theorem Abstract: In this talk, we prove Monsky’s theorem, which states that it is impossible to dissect a square into an odd number of triangles of equal area. The only known proof of Monsky’s theorem uses the concept of valued fields and appears in Aigner and Ziegler’s book Proofs from THE BOOK. 09\/07\/2026 […]<\/p>\n","protected":false},"author":5114,"featured_media":0,"parent":55,"menu_order":-2,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-1208","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages\/1208","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=1208"}],"version-history":[{"count":8,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages\/1208\/revisions"}],"predecessor-version":[{"id":1253,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages\/1208\/revisions\/1253"}],"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=1208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\n\n\n09\/07\/2026 – Chen-Kuan Lee: The Hopf product conjecture<\/h2>\n\n\n\n
\n\n\n\n09\/14\/2026 – Tony Yan: A Taste of Free Probability<\/h2>\n\n\n\n
\n\n\n\n09\/21\/2026 – Atticus Stonestrom: A case against AI use in mathematics<\/h2>\n\n\n\n
\n\n\n\n09\/28\/2026 – Tan \u00d6zalp: TBA<\/h2>\n\n\n\n
\n\n\n\n10\/05\/2026 – Akash Narayanan: TBA<\/h2>\n\n\n\n
\n\n\n\n10\/12\/2026 – Fuxiang Yang: TBA<\/h2>\n\n\n\n
\n\n\n\n10\/19\/2026 – FALL BREAK: NO TALK<\/strong><\/h2>\n\n\n\n
\n\n\n\n10\/26\/2026 – Noa Hunter: TBA<\/h2>\n\n\n\n
\n\n\n\n11\/02\/2026 – Yuyan He: TBA<\/h2>\n\n\n\n
\n\n\n\n11\/09\/2026 – Dominic Scarcelli: TBA<\/h2>\n\n\n\n
\n\n\n\n11\/16\/2026 – Leon Menger: TBA <\/h2>\n\n\n\n
\n\n\n\n11\/23\/2026 – Luis Atzin Franco-Reyna: TBA<\/h2>\n\n\n\n
\n\n\n\n11\/30\/2026 – Emma Dooley: TBA<\/h2>\n\n\n\n
\n\n\n\n12\/07\/2025 – Audriana Houtz: TBA<\/h2>\n\n\n\n