## Simon Felten

I am a post-doc currently based at Columbia University, New York. Most of my work is in logarithmic deformation theory and applications to mirror symmetry.

### The Degeneration of the Smooth Quartic Surface

**P**

^{2}in projective space

**P**

^{3}arranged like a tetrahedron. Indeed they are the four coordinate planes, so their union is defined by the homogeneous equation

*xyzw = 0*in

**P**

^{3}. Let us denote this union by

*D*. We obtain the four planes

*D*as a degeneration of the smooth quartic surface

*E*in

**P**

^{3}which is defined by the equation

*x*in

^{4}+ y^{4}+ z^{4}+ w^{4}= 0**P**

^{3}. This means we have a total space

*X*= {

*sxyzw - t(x*} in

^{4}+ y^{4}+ z^{4}+ w^{4}) = 0**P**

^{1}x

**P**

^{3}

**P**

^{1}x

**P**

^{3}are ([

*t:s*],[

*x:y:z:w*]), and we have a map

*f: X*→

**P**

^{1}given by the first projection. The degenerate surface

*E*is the fiber

*f*

^{-1}(0) whereas the smooth surface

*E*is the fiber

*f*

^{-1}(∞). It is deformed via the intermediate fibers

*f*

^{-1}(

*t*) into

*D*as

*t*→0. The 24 marked points in the picture are the singularities of the total space

*X*. Indeed this variety is (in a neighbourhood of

*D*) smooth everywhere except in these points. When we consider

*f*via

*f*: (

*X,D*)→(

**P**

^{1},

*0*) as a morphism of pairs (or more fancily of logarithmic schemes), these 24 points become the locus where

*f*is not logarithmically smooth. Treating such singularities of logarithmic maps is the starting point for the theory of log toroidal families which I developed in my PhD thesis. This theory is a partial generalization of toric degenerations as studied thoroughly by Gross-Siebert and others. You can find more information about the example in the introduction of my Master Thesis.

### Education

#### PhD Studies

Mathematics, Johannes-Gutenberg-Universität Mainz

*January 2017 - January 2021*

Title: Log Toroidal Families

Advisor: Helge Ruddat

#### Master Studies

Mathematics with minor subject Theoretical Physics, Johannes-Gutenberg-Universität Mainz * October 2015 - July 2018*

Degree: Master of Science

Thesis: Good Differential Forms for a Family of Schemes

Advisor: Helge Ruddat

#### Bachelor Studies

Mathematics with minor subject Theoretical Physics, Johannes-Gutenberg-Universität Mainz *April 2013 - January 2016*

Degree: Bachelor of Science

Thesis: Normal Structures, Cohomology with Supports and Logarithmic Differential Forms

Advisor: Helge Ruddat

Mathematics, Technische Universität Kaiserslautern *October 2011 - March 2012*

#### Early Education

Secondary School, Gymnasium Saarburg *2005 - 2013*

Primary School, Grundschule Irsch *2001 - 2005*

Irsch is a quiet village at the Saar river near the German-Luxemburg border.

### Awards and Scholarships

PhD Scholarship of the German National Academic Foundation

(Promotionsstipendium der Studienstiftung des deutschen Volkes)*April 2017 - March 2020*

PhD Scholarship of the Carl-Zeiss Foundation

(Promotionsstipendium der Carl-Zeiss-Stiftung)*January 2017 - March 2020*

Award for Excellent Master Theses of JGU Mainz

(Preis des Gutenberg-Lehrkollegs für herausragende Abschlussarbeiten)*February 2019*

Leadership Team Award of JGU Mainz*January 2018*

Scholarship of the German National Academic Foundation

(Stipendium der Studienstiftung des deutschen Volkes)*April 2013 - December 2016*

Cowinner of the German National Mathematics Competition

(Bundessieger des Bundeswettbewerbs Mathematik)*January 2013*

Thomas-Morus Award for excellent achievement in Latin and Greek

(Thomas-Morus-Preis für herausragende Leistungen in Latein und Griechisch)*2011*

### Publications / Preprints

You can find my articles also on the arXiv and on Google Scholar .

- Deformations of log Calabi-Yau pairs can be obstructed (with Andrea Petracci and Sharon Robins)
Preprint

- Log Toroidal Families
PhD Thesis available at Gutenberg Open Science

- The Logarithmic Bogomolov-Tian-Todorov Theorem (with Andrea Petracci)
Bull. Lond. Math. Soc. 54 (2022), no. 3, 1051 - 1066.

- Log Smooth Deformation Theory via Gerstenhaber Algebras
manuscripta math. (2020)

- Smoothing Toroidal Crossing Spaces (with Matej Filip, Helge Ruddat)
Forum of Mathematics, Pi (2021) Vol. 9, e7

- Good Differential Forms for a Family of Schemes
Master Thesis

- A Diophantine Equation for Sums of Consecutive Like Powers (with Stefan Müller-Stach)
Elem. Math. 70 (2015), no. 3, 117–124

### Posters

- Good Differential Forms for a Singular Family of Schemes
This is a poster from 2018 explaining my master thesis.

- Almost Log Smooth Families in the Gross-Siebert Program and Beyond
This is a poster from 2017 explaining my PhD project in an early stage.

### Others

- Aus dem Leben eines Mathematikers
This is a Science Slam Talk in German. I describe the life of a PhD student in Mathematics.

- Wie man neue Begriffe einführt ...
This article in German is directed at a general scientific audience and explains my PhD project. It has been written in 2017 when I just begun my PhD.

### Miscellanea

- I did my PhD in Helge Ruddat's Emmy Noether Research Group, based at JGU Mainz.
- This is my profile on MathSciNet.

### Contact

Simon Felten

Department of Mathematics

Columbia University

2990 Broadway

New York, NY 10027

United States

felten.math@posteo.net