Organized by Andrew Navruzyan. Fridays 11am-12:15pm, Room 622 @Mathematics Hall
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Spring seminars:
2/7
Speaker: Shiv Yajnik
Title: More on Complex Geometry
Abstract: TBA
2/14
Speaker: Andrew Navruzyan
Title: String theoretic origins of Gromov-Witten invariants
Abstract: I will give a physical definition of a topological quantum field theory and we will focus in on explicit computations in two such theories: A and B model topological strings. These arise as "twists" of the standard 2-dimensional supersymmetric sigma model and exhibit a celebrated physical duality called mirror symmetry: roughly put, for a given Calabi-Yau 3-fold X, there exists a mirror X^ such that A(X) = B(X^) as TQFTs. This relationship has led to remarkable predictions in enumerative geometry. (Disclaimer: path integration will occur)
3/28
Speaker: Luca Nashabeh
Title: The Topology of Anomalous Hall Insulators
Abstract: Topology is an increasingly powerful tool in condensed matter physics, concisely explaining the macroscopic manifestations of quantum phenomena observed in systems such as quantum Hall insulators and superconductors. In this talk, we will introduce a class of systems—anomalous Hall/Chern insulators—where topology is an essential aspect of their behavior. In particular, we will see how the first Chern class naturally arrises as a characterization of electron bands in a 2d insulator, and how this forces the existence of conducting states at the boundary.
Fall seminars:
11/8
Speaker: Andrew Navruzyan
Title: Classical aspects of bosonic sigma models
Abstract: I will introduce the Nambu-Goto and Polyakov actions and describe their classical solutions and symmetries. By the introduction of the lightcone gauge, we'll see the precise sense in which the transverse vibrations of a physical string give rise to its internal energy. I'll emphasize how this perspective sits in the framework of special/general relativity.
11/15
Speaker: Andrew Navruzyan
Title: Quantum aspects of the free bosonic string
Abstract: We'll wrap up our discussion on the classical phase space of the string and discuss what it means to quantize the string - the discussion will be informal and aim to convey physical intuition. We'll pursue quantization in the light-cone gauge and will develop multiple arguments for the critical dimension D=26 of the target spacetime. We'll also see the particle content of the model - namely why there is a graviton. Finally, due to the general philosophy of quantization commuting with reduction, comments will be made on the so called canonical quantization of the string: the no-ghost theorem of Goddard–Thorn exists within this framework.
11/25 @8pm *note different day and time*
Speaker: Shiv Yajnik
Title: Towards Calabi-Yau Manifolds
Abstract: Calabi-Yau (CY) manifolds are a remarkable subset of Kähler manifolds - special geometries simultaneously possessing three fundamental structures: Riemannian, complex, and symplectic. We will begin by exploring fundamentals of complex and symplectic geometry. Then, I will address the equivalent characterizations of Kähler manifolds, including the existence of the Kähler form. Finally, I will introduce the monumental result in Kähler geometry that gave rise to CY manifolds in the first place.
11/29
No meeting: Thanksgiving Break
12/6
Speaker: Luca Nashabeh
Title: The Hall Effect and Chern-Simons Theory
Abstract: The Hall effect is a simple classical result of electromagnetism: magnetic fields create effective transverse resistivity. In the quantum regime, this effect is discretized, with clean integer jumps. Remarkably however, this discretization is robust to disorder—unlike most quantum effects—allowing the quantum Hall effect to emerge at macroscopic scales. We will endeavor to explain this robustness as resulting from the topology of Chern-Simons field theory. Time permitting, we will also explore the zero magnetic-field anomalous variant of the Hall effect and its similar topological origins.