PhD Candidate: Mehmet Durlanik

Supervisor: Arul Shankar

Thesis title:

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The draft of the thesis can be found here:

]]>PhD Candidate: Mateusz Olechnowicz

Co-Supervisors: Jacov Tsimerman/Patrick Ingram

Thesis title:

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The draft of the thesis can be found here:

]]>PhD Candidate: David Miyamoto

Supervisor: Yael Karshon

Thesis title:

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The draft of the thesis can be found here:

]]>PhD Candidate: Jesse Frohlich

Supervisor: Dror Bar-Natan

Thesis title:

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The draft of the thesis can be found here:

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Zoom Web Conference

PhD Candidate: Sina Zabanfahm

Co-Supervisors: Michael Groechenig/Lisa Jeffrey

Thesis title:

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The draft of the thesis can be found here:

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Zoom Web Conference

PhD Candidate: Peter Angelinos

Supervisor: Michael Groechenig

Thesis title: p-adic Integration for Derived Equivalent Abstract Hitchin Systems

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The draft of the thesis can be found here: angelinos-thesis-draft

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PhD Candidate: Gaurav Patil

Supervisor: V. Kumar Murty

Thesis title: Rings of finite rank over integers

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The draft of the thesis can be found here:

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PhD Candidate: Eva Politou

Supervisor: Stefanos Aretakis

Thesis title: A Geometric Framework for Conservation Laws Along Null

Hypersurfaces and their Relation to Huygens’ Principle

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In the present thesis we examine two main topics. In the first part, we use the general theory of local conservation laws for arbitrary partial differential equations to provide a geometric framework for conservation laws on characteristic null hypersurfaces. The operator of interest is the wave operator on general four-dimensional Lorentzian manifolds restricted on a null hypersurface. In the second part of the thesis, we investigate relations between the geometric conditions that lead to the validity of Huygens’ principle and those that give rise to conservation laws along null hypersurfaces for the wave operator. We apply our results in spacetimes such as the Minkowski, Schwarzschild, and Reissner-Nordström, as well as in general spherically symmetric spacetimes.

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The draft of the thesis can be found here: Eva’s Thesis

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PhD Candidate: Pavel Shlykov

Supervisor: Alexander Braverman

Thesis title: Certain cases of Hikita-Nakajima conjecture

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The draft of the thesis can be found here: thesis_template_shlykov

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PhD Candidate: Faisal Al-Faisal

Supervisor: Steve Kudla

Thesis title: An arithmetic-geometric reciprocity between theta functions

attached to real and imaginary quadratic fields

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We use the theta correspondence to construct classical holomorphic modular forms associated to ideal classes in quadratic number fields. These modular forms are theta functions that were originally introduced by Hecke in the 1920s and have been investigated by several authors since. Our framework allows us to prove old and new results concerning the periods of these modular forms over certain geometric cycles defined by arithmetic data. In particular, we establish a reciprocity relationship between the periods of theta functions attached to ideal classes in real and imaginary quadratic fields. This provides an analogue of (and context for) Hecke’s discovery that certain periods of his imaginary quadratic theta functions are special values of classical Eisenstein series at CM points.

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The draft of the thesis can be found here: alfaisal_thesis

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