Why, What, hoW?

Korea Institute for Advanced Study

Mondays, 16:00 – 17:00 (UTC+9), Online

This seminar is inspired by Idiot's Guide seminar and the New Member Seminar that used to be held at KIAS. Research talks often focus on *what* and *how*, but don't address the question of *why* the speaker finds the topic interesting. By encouraging speakers to avoid technical details and think about *why*, we hope to create a friendly seminar where:

- All members of KIAS and visitors feel welcome.
- Members can learn about areas of mathematics from a down-to-earth perspective.
- Speakers can share the topics they are interested in with a wide audience.
- People from all research areas can socialize.

We invite anyone interested in giving a talk to contact one of the organizers.

This seminar is oriented not to be a usual research seminar. We request that speakers avoid technical details and make the topic accessible to broader audience. Speakers may find it helpful to keep in mind the three questions suggested by the title of the seminar:

*"Why is it interesting to study this topic?"**"What are the main ideas in this topic?"**"How does one study this topic?"*

Speakers may present their own theorems but it is neither necessary nor recommended. As we encourage stupid questions and a lively discussion, speakers should expect less material than in a usual research seminar.

Feel free to contact us at threeW.kias [at] gmail.com

Based on KIAS guidelines to prevent the spread of COVID-19, the seminar will now be held **online**. If you would like to participate, please contact us at threeW.kias [at] gmail.com.

This page uses MathJax. This may cause math processing errors in older browsers such as Internet Explorer 8. If there is a problem, please visit the official announcement of seminars from KIAS.

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July 06:
Jongbaek Song (KIAS)
**
16:00–17:00 (UTC+9) #Zoom

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Toric varieties and Hessenberg varieties
*

A nilpotent Hessenberg variety and a semisimple Hessenberg variety with fixed Hessenberg function have a cohomological relationship, namely the cohomology ring of the former is isomorphic to the ring of invariant of the latter with respect to the symmetric group action. One extreme case of this relationship is given by Peterson varieties and permutohedral varieties, where the latter are smooth toric varieties. In this talk, we introduce a certain class of toric varieties having orbifold singularities and discuss how these objects interact with Hessenberg varieties from the cohomology ring point of view.

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July 13:
Hyun Kyu Kim (Ewha Womans University)
**
11:00–12:00 (UTC+9) #Zoom

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Intertwining operators for representations of quantum varieties
*

A variety can be viewed as a groupoid, whose objects are some commutative algebras, and morphisms are isomorphisms between fields of fractions of the algebras, which are birational maps gluing the affine varieties corresponding to the objects. A quantum variety is a similar groupoid, whose objects are non-commutative deformations of the commutative ones. Then one would want to have a representation of this groupoid on some category of Hilbert spaces. The morphisms are represented by unitary operators that intertwine the representations of the objects. Often, we only need a projective representation of the groupoid, and the lack of it being an ordinary representation yields a 2-cocycle of the groupoid, which sometimes has an interesting interpretation. In this talk I will give an introductory formulation of the above, and go over a couple of examples, about (Segal-)Shale-Weil metaplectic representation of symplectic groups, and about mapping class group representations from quantum Teichmüller theory.

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July 20:
Lavneet Janagal (KIAS-Physics)
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16:00–17:00 (UTC+9) #Zoom

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Sphere packing in higher than 3-D
*

I will discuss few best known sphere packings in higher dimensions with special emphasis on the ones which are proved to be optimal packings in $D=8$ and $D=24$.

References:

1. Sphere packings, Lattices and groups by Conway and Sloane.

2. Sphere packing and quantum gravity (arxiv:1905.01319)

**
July 27:
Benito Juárez-Aubry (IIMAS UNAM)
**
10:00–11:00 (UTC+9) #Zoom

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Quantum field theory in curved spacetimes: What, why and how?
*

Quantum field theory in curved spacetime is a vibrant field of research in physics, lying at the intersection of quantum theory, gravitation and mathematical physics. I will give my perspective on this field, an overview of its conceptual status inside physics and discuss some of the predictions of the theory, such as Hawking radiation and the Unruh effect. I will also comment on mathematical and experimental challenges lying ahead of the road on the subject. In the spirit of the seminar, the talk will be rather verbose and technicalities will be avoided.

Sreedhar Bhamidi, Jean-Emile Bourgine, Sanghyeon Lee, Matthieu Sarkis, Carlos Scarinci

- Makoto Miura
- Plinio Murillo
- Thomas Goller
- Byungdo Park