Time and Location

Mon 2 -5 pm: Math 731

Tue 2-3.30, 4.40-5.30, Math 431

- Joshua Zahl (UBC, Vancouver), Mon 2-2.50 pm, Math 731.

Title: A discretized Severi theorem

Abstract: Severi's theorem classifies 3-dimensional hypersurfaces that contain many lines. I will discuss a discretized variant of this theorem, which classifies hypersurfaces whose thin neighborhood contains many line segments. This problem has applications to questions in harmonic analysis, such as the Kakeya and restriction problems.

- Marie-Francoise Roy (Universite de Rennes 1), Mon 3-3.50, Math 731.

Title: Quantitative fundamental theorem of algebra

Abstract: Using subresultants, we modify a recent proof due to Eisermann of the Fundamental Theorem of Algebra (FTA) to obtain the following quantitative information: in order to prove the FTA for polynomials of degree d, the Intermediate Value Theorem (IVT) is requested to hold for real polynomials of degree at most d^2. We also remind that the classical proof due to Laplace requires IVT or real polynomials of exponential degree. These quantitative results highlight the difference in nature of these two proofs. (Joint work with Daniel Perrucci)

- Andrei Gabrielov (Purdue), Mon 4-4.50, Math 731.

Title: Bi-Lipschitz classification of surface germs

Abstract.

- Abhiram Natarajan (Purdue), Tues 2-2.40 pm, Math 431.

Title: Zeroes of polynomials on definable hypersurfaces: pathologies exist, but they are rare.

Abstract.

- Andrei Gabrielov (Purdue), Tue 4.40-5.30, Math 431.

Title: Ambient Lipschitz equivalence of real surface singularities

Abstract: We present a series of examples of pairs of singular semialgebraic surfaces (germs of real semialgebraic sets of dimension two) in ${\bf R}^3$ and ${\bf R}^4$ which are bi-Lipschitz equivalent with respect to the outer metric, ambient topologically equivalent, but not ambient Lipschitz equivalent. For each singular semialgebraic surface $S\subset {\bf R}^4$, we construct infinitely many semialgebraic surfaces which are bi-lipschitz equivalent with respect to the outer metric, ambient topologically equivalent to $S$, but pairwise ambient Lipschitz non-equivalent. (joint work with Lev Birbrair)