skew product<\/em> which allows for applications to complex dynamics in two dimensions.<\/p>\n\n\n\n
\n\n\n\n10\/24\/2022 – Panel on non-academic jobs<\/h3>\n\n\n\n
This seminar will be a panel discussion featuring four Notre Dame PhD’s in mathematics who are currently working in a job outside of academia, or in academia but not as a math professor.
The panelists are:
Ben Jones ( Notre Dame PhD, 2007, Senior Applied Scientist at Amazon Web Services, Portland)
Ben Lewis (Notre Dame PhD, 2017, Data Scientist at Shopify)
Jeremy Mann (Notre Dame PhD, 2020, Senior Data Scientist at Concert AI, Oakland, CA)
Taylor Ball (Notre Dame PhD, 2021)<\/p>\n\n\n\n
The purpose of this panel discussion is to give current Notre Dame students and other interested parties a better idea of career options outside of academia after getting a math PhD. Each panelist will discuss their own career path and useful skills to develop for getting a teaching position or a job in industry. This is the second in a series of annual panel discussions and we hope that the panelists and others can serve as useful resources for Notre Dame math students interested in working outside of academia.<\/p>\n\n\n\n
\n\n\n\n10\/31\/2022 – Bridget Schreiner: Representation stability for ordered configuration spaces<\/h3>\n\n\n\n
Let \\(\\mathrm{Conf}(n, M) = \\{(x_1, \\dotsc, x_n) \\in M^n: x_i \\neq x_j\\}\\) denote the space of ordered configurations of n points in a manifold \\(M\\). The nth symmetric group acts on this space by permuting the coordinates. When M is a non-compact manifold without boundary, we have maps \\(\\mathrm{Conf}(n, M) \\to \\mathrm{Conf}(n+1, M)\\) by “adding a point near infinity”, inducing maps on homology \\(H_q \\mathrm{Conf}(n, M) \\to H_q \\mathrm{Conf}(n+1, M)\\). These maps do not satisfy homological stability, that is, they are not isomorphisms for \\(n >> q\\). However, accounting for the action of the symmetric group, we have a different type of stability called representation stability. This talk will introduce the notion of representation stability and give a proof of stability for configuration spaces in the case that \\(M = \\mathbb{R}^d\\) If time permits, we will also discuss notions of higher stability. <\/p>\n\n\n\n
\n\n\n\n11\/14\/2022 – Brian Reyes: An introduction to weak solutions<\/h3>\n\n\n\n
In this talk we will see what are weak solutions with some examples starting from the idea of the Fundamental Theorem of Calculus all the way leading up to Sobolev spaces. We will talk about the importance of the Dirac delta function and how the ability to exchange integration with differentiation is crucial in analysis. Integration by parts together with the idea of test functions is one that nowadays is standard but is actually not that old since it was developed in the last century. Finally we talk about how weak solutions relate to real solutions via regularity with a general overview of the usage in PDE.<\/p>\n\n\n\n
\n\n\n\n11\/21\/2022 – Randy Van Why (Princeton): A glance at low dimensional symplectic topology<\/h3>\n\n\n\n
Symplectic geometry is a peculiar geometry from an outsiders perspective. The field has its roots in physics but the theory has expanded far beyond the scope of the conceptual frameworks from the genesis of the field. Currently, there is no wide consensus on what symplectic geometry is, what it is good for, or what it possibly has to say about geometry\/topology in the large. <\/p>\n\n\n\n
In this talk, I hope to introduce everyone to my favorite facet of this enigmatic field: symplectic geometric topology. I will use complex affine varieties as a motivator for discussing some constructions in symplectic 4-manifolds and contact 3-manifolds. If time permits, I will discuss some little known connections between modern symplectic geometry and classical geometric topology. <\/p>\n\n\n\n
\n\n\n\n11\/28\/2022 – Ethan Reed: Using Geometric Methods to Construct Generalized Eagon-Northcott Complexes<\/h3>\n\n\n\n
In Commutative Algebra, Generalized Eagon-Northcott Complexes are a family of complexes that generalize the Koszul Complex. Many properties of these complexes can be proved algebraically, but they can alternatively be proven using algebraic geometric methods. In this talk, we will describe the relevant tools of algebraic geometry and sketch how to use them to construct Generalized Eagon-Northcott Complexes. More specifically, we will use a relative hypercohomology spectral sequence from twists of a Koszul resolution of sheaves on a projectivized bundle to derive the existence of these complexes.<\/p>\n\n\n\n
\n\n\n\n12\/5\/2022 – Lizda Nazdira Moncada Morales: Graphs, Hypergraphs, and their Edge Ideals<\/h3>\n\n\n\n
Classification of minimal free resolutions of monomial ideals is one of the central problems in combinatorial commutative algebra. By polarization, studying the minimal free resolution of a graded monomial ideal is equivalent to studying the minimal free resolutions of a particular class of squarefree monomial ideals: edge ideals. The homological properties of an edge ideal of a (hyper)graph depend on the combinatorial properties of the (hyper)graph. In this talk, we will present a characterization of some edge ideals which have linear resolutions as well as some results on their regularity and Betti numbers. <\/p>\n","protected":false},"excerpt":{"rendered":"
8\/29\/2022 – Hari Rau-Murthy: The tensor product of an algebra with a space You might know how to take the tensor product of two algebras. But the tensor product of an algebra with a space!!! The result is a ring. I will introduce \\(A \\otimes X\\) where \\(A\\) is an algebra and \\(X\\) is a space. The tensor product of \\(A\\) with […]<\/p>\n","protected":false},"author":2271,"featured_media":0,"parent":55,"menu_order":6,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-125","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages\/125","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\/2271"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/comments?post=125"}],"version-history":[{"count":30,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages\/125\/revisions"}],"predecessor-version":[{"id":362,"href":"https:\/\/sites.nd.edu\/mgsa\/wp-json\/wp\/v2\/pages\/125\/revisions\/362"}],"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=125"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}