Talk_id  Date  Speaker  Title 
9251

Wednesday 1/17 4:10 PM

Hitesh Gakhar, MSU

Dualities in Persistent (co)Homology
 Dualities in Persistent (co)Homology
 01/17/2018
 4:10 PM  5:00 PM
 C204A Wells Hall
 Hitesh Gakhar, MSU
For a filtered topological space, its persistent homology is a multiset of half open real intervals known as barcode. Each bar represents the lifespan of a homology class. A fundamental principle is that the length of such a bar determines the significance of the corresponding class. In 2011, V. de Silva et al studied the relationships between (persistent) absolute homology, absolute cohomology, relative homology and relative cohomology. This talk will be a theoretical overview of that study.

9255

Wednesday 1/24 4:10 PM

Hitesh Gakhar, MSU

Dualities in Persistent (co)HomologyPart II
 Dualities in Persistent (co)HomologyPart II
 01/24/2018
 4:10 PM  5:00 PM
 C517 Wells Hall
 Hitesh Gakhar, MSU
For a filtered topological space, its persistent homology is a multiset of half open real intervals known as barcode. Each bar represents the lifespan of a homology class. A fundamental principle is that the length of such a bar determines the significance of the corresponding class. In 2011, V. de Silva et al studied the relationships between (persistent) absolute homology, absolute cohomology, relative homology and relative cohomology. This talk will be a theoretical overview of that study.

9269

Wednesday 2/7 4:10 PM

Eylem Zeliha YILDIZ, MSU

Invertible Knot Concordances
 Invertible Knot Concordances
 02/07/2018
 4:10 PM  5:00 PM
 C204A Wells Hall
 Eylem Zeliha YILDIZ, MSU
In this talk I will give a constructive proof to " Let k be a knot in S1 ×S2 freely homotopic to S1 ×pt then S1 × pt bounds an invertible concordance and k splits (S1 × pt) × [0, 1]."

10275

Wednesday 2/14 4:10 PM

Kumar, Sanjay Lakshman, MSU

Skein Theory and TuraevViro Invariant
 Skein Theory and TuraevViro Invariant
 02/14/2018
 4:10 PM  5:00 PM
 C204A Wells Hall
 Kumar, Sanjay Lakshman, MSU
This talk will be a brief introduction to the TuraevViro Invariant. The TuraevViro Invariant is a 3manifold invariant defined on a triangulation of a manifold. Using skeintheoretic methods, I will demonstrate a proof of its invariance with a technique known as chainmail. This technique illustrates a close relationship between the TuraevViro Invariant and the surgerypresentation invariants originally defined by Reshetikhin and Turaev.

12283

Wednesday 2/21 4:10 PM

Brandon Bavier, MSU

An Introduction to Hyperbolic Knots
 An Introduction to Hyperbolic Knots
 02/21/2018
 4:10 PM  5:00 PM
 C204A Wells Hall
 Brandon Bavier, MSU
When studying knots, it is common to look at their complement to find invariants of the knot. One way to do this is to put a geometric structure on the complement, and look at common geometric invariants, such as volume. This talk is an introduction to hyperbolic knots, knots whose complement admits a hyperbolic structure. This will include a couple of diagramatic conditions to detect hyperbolicity, as well as using the structure to calculate bounds on the volume of the complement.

13299

Wednesday 3/14 4:10 PM

Wenzhao Chen, MSU

Correction term, diagonalization theorem and the sliceness of 2bridge knots
 Correction term, diagonalization theorem and the sliceness of 2bridge knots
 03/14/2018
 4:10 PM  5:00 PM
 C204A Wells Hall
 Wenzhao Chen, MSU
About a decade ago, Lisca classified which 2bridge knots are smoothly slice using an obstruction derived from Donaldson's diagonaliztion theorem. It is known that the diagonalization theorem can be proved using the Heegaard Floer correction term. Moreover, this correction term can also be used to construct a slicing obstruction for knots. In this expository talk, I will explain Josh Greene's proof that these two slicing obstructions actually coincide for 2bridge knots.

13316

Wednesday 3/28 4:10 PM

Gorapada Bera, MSU

Symplectic Quotients and GIT Quotients : The KempfNess Theorem
 Symplectic Quotients and GIT Quotients : The KempfNess Theorem
 03/28/2018
 4:10 PM  5:00 PM
 C204A Wells Hall
 Gorapada Bera, MSU
The KempfNess theorem is a fundamental result at the intersection of complex algebraic Geometry and Symplectic Geometry .It states the equivalence of Symplectic and Geometric invariant theory quotients. After brief introduction of each of the quotients we will cover the proof of the theorem.

13325

Wednesday 4/4 4:10 PM

Nicholas Ovenhouse, MSU

The Pentagram Map
 The Pentagram Map
 04/04/2018
 4:10 PM  5:00 PM
 C204A Wells Hall
 Nicholas Ovenhouse, MSU
The pentagram map is a discrete dynamical system introduced by Richard Schwartz, which acts on the space of all planar polygons. More generally, the map is defined on the space of all "twisted polygons". In this talk, we will define twisted polygons, and then construct a coordinate system on the space of all twisted polygons, and write a formula for the pentagram map in these coordinates. If there is time, we will discuss a Poisson structure on the space of polygons which can be used to show that the pentagram map is a completely integrable system (in the sense of Liouville).

13334

Wednesday 4/11 4:10 PM

Zhe Zhang, MSU

Spin Geometry, Bochner’s Method, and Vanishing Theorems
 Spin Geometry, Bochner’s Method, and Vanishing Theorems
 04/11/2018
 4:10 PM  5:00 PM
 C204A Wells Hall
 Zhe Zhang, MSU
On a compact Riemannian manifold X, we can give two different Laplace operators, namely the Dirac Laplacian and the Bochner Laplacian. Their difference is of order zero, and can be expressed in terms of the curvature tensor of X. Using harmonic theory, Bochner was able to conclude that the vanishing of certain Betti numbers of X under appropriate positivity assumptions on the curvature tensor.
