Weekly Bulletin
The FIM provides a Newsletter called FIM Weekly Bulletin, which is a selection of the mathematics seminars and lectures taking place at ETH Zurich and at the University of Zurich. It is sent by e-mail every Tuesday during the semester, or can be accessed here on this website at any time.
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Monday, 18 September | |||
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Time | Speaker | Title | Location |
17:15 - 18:15 |
Prof. Dr. Dacheng Xiucall_made Booth School of Business, University of Chicago |
HG D 3.2 |
Tuesday, 19 September | |||
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— no events scheduled — |
Wednesday, 20 September | |||
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— no events scheduled — |
Thursday, 21 September | |||
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— no events scheduled — |
Friday, 22 September | |||
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Time | Speaker | Title | Location |
14:15 - 15:15 |
Dr. Peter Hubrecht Koymanscall_made ETH Zurich, Switzerland |
Abstract
In this talk we will study the negative Pell equation, which is the conic C_D : x<sup>2</sup> - D y<sup>2</sup> = -1 to be solved in integers x, y in Z. We shall be concerned with the following question: as we vary over squarefree integers D, how often is C_D soluble? Stevenhagen conjectured an asymptotic formula for such D. Fouvry and Kluners gave upper and lower bounds of the correct order of magnitude. We will discuss a proof of Stevenhagen's conjecture, and, time permitting, potential applications of the new proof techniques. This is joint work with Carlo Pagano.
Number Theory SeminarThe negative Pell equationread_more |
HG G 43 |
15:15 - 16:15 |
Zijian Guo Rutgers University, USA |
Abstract
Instrumental variable methods are among the most commonly used causal inference approaches to deal with unmeasured confounders in observational studies. The presence of invalid instruments is the primary concern for practical applications, and a fast-growing area of research is inference for the causal effect with possibly invalid instruments. This paper illustrates that the existing confidence intervals may undercover when the valid and invalid instruments are hard to separate in a data-dependent way. To address this, we construct uniformly valid confidence intervals that are robust to the mistakes in separating valid and invalid instruments. We propose to search for a range of treatment effect values that lead to sufficiently many valid instruments. We further devise a novel sampling method, which, together with searching, leads to a more precise confidence interval. Our proposed searching and sampling confidence intervals are uniformly valid and achieve the parametric length under the finite-sample majority and plurality rules. We apply our proposal to examine the effect of education on earnings. The proposed method is implemented in the R package \texttt{RobustIV} available from CRAN.
Research Seminar in StatisticsJoint talk: Robust Causal Inference with Possibly Invalid Instruments: Post-selection Problems and A Solution Using Searching and Samplingread_more |
HG G 19.1 |
15:15 - 16:15 |
Zijian Guo Rutgers University, USA |
Abstract
Instrumental variable methods are among the most commonly used causal inference approaches to deal with unmeasured confounders in observational studies. The presence of invalid instruments is the primary concern for practical applications, and a fast-growing area of research is inference for the causal effect with possibly invalid instruments. This paper illustrates that the existing confidence intervals may undercover when the valid and invalid instruments are hard to separate in a data-dependent way. To address this, we construct uniformly valid confidence intervals that are robust to the mistakes in separating valid and invalid instruments. We propose to search for a range of treatment effect values that lead to sufficiently many valid instruments. We further devise a novel sampling method, which, together with searching, leads to a more precise confidence interval. Our proposed searching and sampling confidence intervals are uniformly valid and achieve the parametric length under the finite-sample majority and plurality rules. We apply our proposal to examine the effect of education on earnings. The proposed method is implemented in the R package RobustIV available from CRAN.
ETH-FDS seminar Joint talk: Robust Causal Inference with Possibly Invalid Instruments: Post-selection Problems and A Solution Using Searching and Sampling read_more |
HG G 19.1 |
16:00 - 17:30 |
Dr. Michele Graffeo Politecnico di Milano |
Abstract
The Hilbert scheme Hilb^nX of n points on a quasi-projective variety X is a geometrical object introduced by Grothendieck and it has a prominent rôle in many areas of algebraic geometry. Recently, many variants of Hilb^nX have been introduced. My talk will focus on the double nested Hilbert scheme of points on X defined by S. Monavari. Specifically, I will explain how, when X is a smooth irreducible curve, its geometry is influenced by the combinatorics of reverse plane partitions and exhibits several pathologies.
This is a joint project with Lella, Monavari, Ricolfi, Sammartano and it is partially funded by: PRIN 2020 “Squarefree Gröbner degenerations, special varieties and related topics” (MUR, project number 2020355B8Y)
Algebraic Geometry and Moduli SeminarThe geometry of double nested Hilbert shemesread_more |
HG G 43 |