Video Content by Date
Speaker: Vinod Vaikuntanathan
Integer lattices play a central role in mathematics and computer science, with applications ranging from number theory and coding theory to combinatorial optimization. Over the past three decades, they have also become a cornerstone of modern cryptography.
In this talk, I will describe the evolution of lattices in cryptography: from the early use of lattices to break classical cryptosystems; to their application in designing new encryption and digital signature schemes with (conjectured) post-quantum security; and to their role in achieving long-standing cryptographic goals such as fully homomorphic encryption that allow us to compute directly on encrypted data.
The talk will not assume any prior background in cryptography.
Speaker: Valentina Zapata Castro
Model categories provide a powerful framework for abstract homotopy theory, but their complexity often makes them difficult to classify. By focusing on finite categories, especially grids, we gain a combinatorial setting where the problem becomes explicit. In this talk, we explore model structures through weak factorization systems (WFS) on posets, which are in one-to-one correspondence with transfer systems and their duals, both introduced here. This perspective leads to a method for constructing model structures and a characterization theorem for finding weak equivalence sets in posets. Our approach offers a pathway towards classifying model structures in a controlled setting.
This is joint work with Kristen Mazur, Angélica Osorno, Constanze Roitzheim, Rekha Santhanam and Danika Van Niel.
