Olivier Martin

University of Chicago · olivier@uchicago.edu

I am a fifth year graduate student at the University of Chicago working with Alexander Beilinson and Madhav Nori. I am interested in algebraic cycles and motives. Before moving to Chicago I did my undergraduate studies at McGill University in Montréal, where I learned a lot from Henri Darmon and Daniel T. Wise. I grew up in Québec city, Canada.


Research

My research currently focuses on the study of the Chow group of zero cycles on abelian varieties. In particular, I have recently given a proof of a conjecture of Voisin on the gonality of very general abelian varieties. Along with other recent works it highlights the geometric significance of orbits for rational equivalence. Notably, in this paper Voisin defines a filtration on the Chow groups of zero-cycles of hyper-Kähler varieties which is conjecturally opposed to the Bloch-Beilinson filtration. This provides a relation between the approaches of Mumford and Roĭtman and the modern viewpoint pioneered by Bloch and Beilinson. I am interested in exploring the connections between these two perspectives on algebraic cycles.

Papers

On a Conjecture of Voisin on the Gonality of Very General Abelian Varieties, Preprint, 27p.

Teaching

During my graduate studies I have taught the following classes at the University of Chicago:


MATH 196 - Linear Algebra

Winter 2018

MATH 196 - Linear Algebra

Fall 2018

MATH 195 - Mathematical Methods for Social Sciences

Spring 2018

MATH 153 - Calculus 3

Fall 2017

MATH 196 - Linear Algebra

Spring 2017

MATH 153 - Calculus 3

Fall 2017

In addition, I was a teaching assistant for the Honors Algebra sequence taught by Madhav Nori and Kevin Corlette in 2015-2016.


Photography

In the past years I have had the occasion to travel to many locations for climbing, hiking, and mountaineering. Here are a few shots of some places that have especially struck me.

La candelle

La Grande Candelle seen from the path between the calanque de Morgiou and the calanque de Sugiton, France (Fall 2018).




La candelle

The Zwischbergen pass, Switzerland (Summer 2017).




La candelle

View from the SE ridge of Weissmies, Switzerland (Summer 2017).




La candelle

Sunrise on Yatsugatake, Japan (Winter 2017).




La candelle

Zion national park, Utah (Fall 2016).




La candelle

þórsmörk, Iceland (Summer 2016).