IMSA Seminar
Dr. Andrew Harder, Lehigh University
Hodge numbers of orbifold Clarke mirrors and mirror symmetry
Thursday, April 18, 2024, 5:30pm
Ungar, Room 528B
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Abstract: Batyrev and Borisov gave a combinatorial mirror construction of dual pairs of toric complete intersections Calabi-Yau varieties coming from nef partitions of reflexive polytypes, and in 1996 they showed that the stringy Hodge Numbers of these pairs satisfy a particular duality predicted by mirror symmetry. Later, Clarke gave a far-reaching combinatorial mirror construction which generalizes the Batyrev-Borisov construction and many other combinatorial mirror constructions.
I'll describe work in progress with Sukjoo Lee (Edinburgh) that uses new tools from tropical geometry to prove Hodge number duality for a large class of Clarke mirror pairs. This immediately recovers Batyrev and Borisov's results and leads to a proof of a conjecture of Katzarkov, Kontsevich, and Pantev for orbifold toric complete intersections. I'll describe how a construction of Doran and Harder, relating Laurent polunoials and singular toric complete intersections, fits into the Clarke mirror framework. As a consequence, my results with Sukjoo lead to predictions related to the Fanosearch Program.
IMSA Seminar
Dr. Zachary Feinstein, Stevens Institute of Technology
Axioms for Automated Market Makers and Decentralized Finance
Tuesday, April 9, 2024, 4:00pm
Ungar, Room 528B
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Abstract: Within this talk, we introduce an axiomatic framework for Automated Market Makers (AM Ms). By imposing reasonable axioms on the underlying utility function, we are able to characterize the properties of the swap size of the assets and of the resulting pricing oracle. We will analyze many existing AM Ms and show that the vast majority of them satisfy our axioms. We will also consider the question of fees and divergence loss. In doing so, we will propose a new fee structure so as to make the AMM indifferent to transaction splitting. Finally, we will propose a novel AMM that has nice analytical properties and provides a large range over which there is no divergence loss.
IMSA Seminar
Stephan Sturm, Associate Professor, Worcester Polytechnic Institute
The Distribution Builder - A tool for financial decision making in the Fin Tech era
Wednesday, March 27, 2024, 4:00pm
Ungar, Room 528B
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Abstract: The era of Fin Tech heralds personalized financial decision making through tools such as robo-advising. Alas, the input of personal. preferences needed to personalize decision making is difficult and existing methods lack robustness. Sharpe, Goldstein, Blythe and Johnson introduced with the distribution builder a powerful tool to directly solicit user preferences on the outcomes of investments that can be used as base from decision making. In this presentation we explain how the methodology of the distribution builder can be leveraged successfully from the original setting· portfolio optimization in complete markets· to a wide array of other situations: consumption, incomplete markets and the timing of asset sales. This talk is based on joint work with Carole Bernard, Peter Carr, Mauricio Elizalde Mejia, Sixian Jin and Benjamin Rajone.
