We show that the three-dimensional homology cobordism group admits an infinite-rank summand. It was previously known that the homology cobordism group contains an infinite-rank subgroup and a Z-summand. The proof relies on the involutive Heegaard Floer homology package of Hendricks-Manolescu and Hendricks-Manolescu-Zemke. This is joint work with I. Dai, M. Stoffregen, and L. Truong.
In this talk, we shall review the Hamilton-Jacobi theory for A Fully Convex Bolza (FCB) problems when the data has no implicit state constraints and is coercive, in which case the minimizing class of arcs are Absolutely Continuous (AC).
His talk concerns the study of criticality of Lagrange multipliers in variational systems that have been recognized in both theoretical and numerical aspects of optimization and variational analysis. In contrast to the previous developments dealing with polyhedral KKT systems and the like, we now focus on general nonpolyhedral systems that are associated, in particular, with…
We discuss the facial weak order, a poset structure that extends the poset of regions on a central hyperplane arrangement to the set of all faces of the arrangement which was first introduced on the braid arrangements by Krob, Latapy, Novelli, Phan and Schwer. We provide various characterizations of this poset including a global one, a local one, one using…
Most algorithms to compute a Gröbner basis are “static”, inasmuch as they require as input both a set of polynomials and a term ordering, and preserve the term ordering throughout the computation. This talk presents ongoing work on “dynamic” Buchberger algorithms. First described by Sturmfels and Caboara, dynamic algorithms require only a set of polynomials…
Join us tomorrow Wednesdays from 12:00-1:00 in the math graduate lounge for our weekly brown bag lunch. As a reminder all are welcomed including undergraduate students!
Crumples in a sheet of paper, wrinkles on curtains, cracks in metallic alloys, and defects in superconductors are examples of patterns in materials. A thorough understanding of the underlying phenomenon behind the pattern formation provides a different prospective on the properties of the existing materials and contributes to the development of new ones. In my talk…
Geneva Collins Title : Automatic Geometric Theorem Proving: Sangaku From an Algebraic PerspectiveAbstract: During the Edo period (1603-1867 CE) Japan was almost completely closed off from the rest of the world and developed its own mathematical tradition called wasan. Part of this tradition was to hang tablets, known as sangaku, in the eaves of a…
For an un-oriented link K, let L(K) be the ropelength of K. It is known that in general L(K) is at least of the order O((Cr(K))3/4), and at most of the order O(Cr(K) ln5 (Cr(K)) where Cr(K) is the minimum crossing number of K. Furthermore, it is known that there exist families of (infinitely many) links with the property…
From ultrasound scanners used before birth to environmental sensors that monitor the pathways of harmful substances, imaging technologies play an important role in human lives. In this workshop, I will explain some of the mathematical ideas behind image reconstructions: how they work, what their limitations are, and what uncertainties are associated with interpreting the images generated by imaging technologies. Bio: Arvind…
The original construction of the Khovanov homology of a link can be seen as a formal complex in the category of flat tangles and surfaces between them. There is a way to associate a chain map with a link cobordism, but only up to a sign. Blanchet has fixed this by introducing the category of gl(2)-foams, certain singular cobordisms…
The Math Graduation Ceremony for Spring 2019 will be held on Friday, May 10th at 10:00am in the McKimmon Center. Directions for the McKimmon Center is located here.