| Talk_id | Date | Speaker | Title |
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19662
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Monday 9/30
3:00 PM
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Keshav Sutrave, MSU
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Some kind of introduction to special relativity
- Keshav Sutrave, MSU
- Some kind of introduction to special relativity
- 09/30/2019
- 3:00 PM - 3:50 PM
- C304 Wells Hall
(Soft) The beginning of Einstein's theory of special relativity, which gives us a way of doing physics in different reference frames (observers in motion). Specifically: "What happens when you turn on a flashlight while already moving at half the speed of light?" I will introduce time dilation and length contraction, event simultaneity, and touch on the problem in electromagnetism, using many examples.
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19653
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Monday 10/7
3:00 PM
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Joe Melby, MSU
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Complexity, 3-Manifolds, and Zombies
- Joe Melby, MSU
- Complexity, 3-Manifolds, and Zombies
- 10/07/2019
- 3:00 PM - 3:50 PM
- C304 Wells Hall
An important invariant of a path-connected topological space X is the number of homomorphisms from the fundamental group of X to a finite, non-abelian, simple group G. Kuperberg and Samperton proved that, although these invariants can be powerful, they are often computationally intractable, particularly when X is an integral homology 3-sphere. More specifically, they prove that the problem of counting such homomorphisms is #P-complete via a reduction from a known #P-complete circuit satisfiability problem. Their model constructs X from a well-chosen Heegaard surface and a mapping class in its Torelli group. We will introduce the basics of complexity for counting problems, summarize the reduction used by K-S to bound the problem of counting homomorphisms, and discuss some of the topological and quantum computing implications of their results.
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19654
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Monday 10/14
3:00 PM
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Zhe Zhang, MSU
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An introduction to intersection forms: Taking K3 surface as an example
- Zhe Zhang, MSU
- An introduction to intersection forms: Taking K3 surface as an example
- 10/14/2019
- 3:00 PM - 3:50 PM
- C304 Wells Hall
I’ll define intersection product both on 4 manifolds and in the algebraic geometry setting, then introduce the blow up technique and give some easy examples. After that I will jump to K3 surface, give definition and constructions, and talk a little bit about the elliptic fibrations of K3. If I still have time, I will talk about the relation between intersection form and characteristic classes.
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19655
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Monday 10/21
3:00 PM
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Brandon Bavier, MSU
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The Ends of Hyperbolic Manifolds
- Brandon Bavier, MSU
- The Ends of Hyperbolic Manifolds
- 10/21/2019
- 3:00 PM - 3:50 PM
- C304 Wells Hall
When studying knots, we can often get a lot of information by removing the knot from space, and looking at the knot complement. It's pretty natural to ask, then, what happens to the area close to the removed knot? We call these areas cusps, and, in the case of hyperbolic knots, the cusp alone can tell us quite a lot. In this talk, we will give an introduction to these cusps, including their uses in topology, as well as how to find invariants from them.
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19656
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Monday 10/28
3:00 PM
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Arman Tavakoli, MSU
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Introduction to the Yang-Mills equation
- Arman Tavakoli, MSU
- Introduction to the Yang-Mills equation
- 10/28/2019
- 3:00 PM - 3:50 PM
- C304 Wells Hall
The Yang-Mills equation is a celebrated topic that is studied in differential geometry and particle physics. We will motivate the equation as a generalization of Maxwell's equations, define the relevant geometrical objects and discuss their properties.
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19657
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Monday 11/4
3:00 PM
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Gorapada Bera, MSU
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Introduction to Riemannian Holonomy
- Gorapada Bera, MSU
- Introduction to Riemannian Holonomy
- 11/04/2019
- 3:00 PM - 3:50 PM
- C304 Wells Hall
The holonomy group of a Riemannian manifold exhibits various geometric structures compatible with the metric. In 1955, M.Berger classified all possible Riemannian holonomy groups. Studying all these are more than one semester subject. So, in this talk after a brief introduction we overview very basics of these holonomy groups.
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19658
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Monday 11/11
3:00 PM
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Wenchuan Tian, MSU
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Properties of Busemann function on manifolds with nonnegative sectional curvature outside of a compact set
- Wenchuan Tian, MSU
- Properties of Busemann function on manifolds with nonnegative sectional curvature outside of a compact set
- 11/11/2019
- 3:00 PM - 3:50 PM
- C304 Wells Hall
Busemann functions are useful. Cheeger and Gromoll used them to prove the splitting theorem for manifolds with nonnegative ricci curvature that contains a line. Yau used them to prove that complete noncompact manifolds with nonnegative Ricci curvature have at least linear volume growth.
In a paper called "Positive Harmonic Functions on Complete Manifolds with Non-Negative Curvature Outside a Compact Set" Peter Li and Luen-Fai Tam also used Busemann function to show the existence of positive harmonic functions. I will talk about Li and Tam's proof of properties of Busemann function. The proof only uses Toponogov theorem and cosine law. The results of the proof is useful for the subsequent analysis part of the paper.
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19659
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Monday 11/18
3:00 PM
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Sarah Klanderman, MSU
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Computations in Topological CoHochschild Homology
- Sarah Klanderman, MSU
- Computations in Topological CoHochschild Homology
- 11/18/2019
- 3:00 PM - 3:50 PM
- C304 Wells Hall
Hochschild homology (HH) is a classical algebraic invariant of rings that can be extended topologically to be an invariant of ring spectra, called topological Hochschild homology (THH). There exists a dual theory for coalgebras called coHochschild homology (coHH), and in recent work Hess and Shipley defined an invariant of coalgebra spectra called topological coHochschild homology (coTHH). In this talk we will discuss coTHH calculations and the tools needed to do them.
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19661
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Monday 12/2
3:00 PM
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Sanjay Kumar, MSU
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An Introduction to Link Invariants from Tangle Operators
- Sanjay Kumar, MSU
- An Introduction to Link Invariants from Tangle Operators
- 12/02/2019
- 3:00 PM - 3:50 PM
- C304 Wells Hall
In the early 90’s, Reshetikhin and Turaev constructed topological invariants of 3-manifoolds and of framed links in 3-manifolds using quantum groups. In this talk, I will introduce their approach with specific examples and show how they relate to known link invariants such as the Jones polynomial.
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