**2024년 03월 QSMS Monthly Seminar **

**Date:**Mar. 22th (Fri) 14:00 ~ 17:00**Place:**27-220 (SNU)**Contents:**

**Speaker: ** 이석형 (SNU)

**Title: **Lifting problem for universal quadratic forms

**Abstract**: A positive definite quadratic form is called universal if it can represent all nonnegative integers, such as the form $x^2+y^2+z^2+w^2$ as shown by Lagrange. The concept of "lifting problem" generalizes this notion to totally real number fields $K$: an integral quadratic form is called universal over $K$ if it can represent every total positive integral element. In this talk, we survey several results on universal forms over number fields, especially focusing on some recent developments obtained by utilizing the geometry of numbers argument. Then we present our result classifying all cubic and biquadratic fields which admit an integral universal form. This is joint work with Daejun Kim.

**Speaker: **강정수 (SNU)

**Title: **Poincare duality in Rabinowitz Floer homology

**Abstract**: A recent study by Cieliebak and Oancea discovers a Poincare duality property in Rabinowitz Floer homology, which resolves several mysterious duality phenomena in String topology. I will give a gentle introduction to this recent development.