Hello,

The Department of Mathematical Sciences at Seoul National University, under the 10-10 project, will host the 4th Gauss Scholar Lecture featuring Prof. Byung-Han Kim from the Department of Mathematics at Yonsei University. We kindly invite you to participate. Thank you.

• Date:

  • November 4, 2024 (Monday), and November 8, 2024 (Friday), from 16:00 to 17:30 (including Q&A)

• Location:

  • Seoul National University, Building 129, 1st floor, Sangsan Mathematical Sciences Building

• Lecture Information:

  • November 4 (Monday), 16:00-17:30 (including Q&A)

    • Title: Compactness and ultraproducts in model theory.
    • This lecture will introduce Gödel's compactness theorem, which forms the foundation of model theory in mathematical logic, and will prove it using the concept of ultraproducts. Applications will include results such as Prof. Jung Wook Lee’s findings on necessary and sufficient conditions for the existence of an upper bound on the rank of elliptic curves defined over number fields, and Ax’s results on pseudo finite fields (ultraproducts of finite fields).

  • November 8 (Friday), 16:00-17:30 (including Q&A)

    • Title: Model theoretic studies on the real/complex fields, with exponentiation.
    • The model-theoretic study of real fields has a long history. In particular, Tarski’s result that real closed ordered fields have quantifier elimination is a cornerstone. This lecture will present this proof and use it to derive Hilbert’s 17th problem (the statement that every positive definite rational function over the real field is a sum of squares of rational functions) easily. The talk will also introduce model-theoretic studies by Wilkie on structures with exponentiation, which contributed to solving the Andre-Oort conjecture. If time allows, Zilber’s model-theoretic studies on complex fields with exponentiation and Schanuel’s conjecture will also be discussed.