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The Fields-Carleton Distinguished Lecture is annual lecture sponsored by the Fields Institute and Carleton University featuring international-renowned speakers with expertise in mathematics, statistics and theoretical computer science. Recent guest speakers include Uffe Haagerup (University of Copenhagen); Thomas C. Hales (University of Pittsburgh); Kenneth R. Davidson (University of Waterloo); Donald Dawson (Carleton University); V. Kumar Murty (University of Toronto); Philippe Flajolet (INRIA); Jerrold Marsden (California Institute of Technology); and, Donald Saari (University of California, Irvine).

Each guest speaker delivers a public lecture as well as a **Research Lecture**, which is more technical in nature.

## Public Lecture

### Dr. Gang Tian

Chair, Professor, and Vice President

Peking University

*Poincaré Conjecture and Geometrization*

*Poincaré Conjecture and Geometrization*

**Thursday, April 5, 2018**

6:30 p.m. Reception; 7:00 p.m. Lecture

Hamelin Hall (MHN 257), University of Ottawa, 70 Laurier Avenue East

6:30 p.m. Reception; 7:00 p.m. Lecture

Hamelin Hall (MHN 257), University of Ottawa, 70 Laurier Avenue East

##### IMPORTANT PARKING UPDATE:

Please note that parking permits are available ONLY for Desmarais indoor parking, or outdoor parking Lot C.

Participants can print a parking permit here.

Register hereFor more than one hundred years, the Poincaré conjecture was a driving force for topologists and its study led to many important advances in the area. It was finally solved by Perelman using differential geometric methods. In this lecture, Dr. Gang Tian will introduce the Poincaré conjecture and give a brief history of its mathematical pursuit. He will explain some of the geometric ideas involved in solving the conjecture, in particular, the geometrization of 3-spaces. The talk will end with some speculations on future developments in geometry. This lecture is aimed at general audience.

## Research Lecture

*Introduction to Geometric Flows*

**Monday, April 9, 2018**

10:30 a.m.

MacPhail Room, 4351 Herzberg Laboratories

10:30 a.m.

MacPhail Room, 4351 Herzberg Laboratories

In this expository talk, Dr. Tian will give a brief tour on geometric flows. He will start with Ricci flow and discuss some of its applications in geometry. He will then discuss some new geometric flows introduced more recently, and show how they can be applied to studying geometry of manifolds. Finally, Dr. Tian will present some recent results and open problems.

## About the speaker

Dr.Gang Tian has made fundamental contributions to geometric analysis, complex geometry and symplectic geometry. He did his undergraduate study at Nanjing University in China, received his MS at Peking University and PhD at Harvard University. He was a professor at Courant Institute of NYU, a Simons professor at MIT and a Higgins professor at Princeton University. He is now a Chair professor and Vice President of Peking University. Dr. Gang Tian solved completely the existence of Kahler-Einstein metrics on compact complex surfaces with positive first Chern class. He proved that the deformation of Calabi-Yau manifolds is unobstructed, now known as the Bogomolov–Tian–Todorov theorem. Together with Ruan, he established a mathematical theory for quantum cohomology and Gromov-Witten invariants on semi- positive symplectic manifolds which include any symplectic manifolds of dimension 3 and Calabi-Yau spaces, in particular, they proved the associativity of the quantum cohomology ring of semi-positive symplectic manifold. He was also one of pioneers in constructing virtual cycles and consequently constructed the Gromov-Witten invariants for any closed symplectic manifolds. He developed a compactness theory for high dimensional Yang-Mills fields and found a deep connection between high dimensional gauge fields and calibrated geometry. He introduced the K-stability which has been further developed and become a central topic in the theory of geometric stability. He initiated the Analytical Minimal Model program through Kahler-Ricci flow, known as Tian-Song MMP theory in complex geometry. Together with J. Morgan, amongst others, Dr. Gang Tian played a very important role in the solution of Poincaré Conjecture and Thurston’s Geometrization Conjecture by providing sufficient arguments in the proof by G. Perelman. More recently, he gave a complete solution for the Yau-Tian-Donaldson's conjecture, a central conjecture in Kahler geometry. His solution follows the approach he proposed before. Together with J. Streets, he introduced new geometric flows and found their connection to the duality in the superstring theory. Their flows provide very important tools in complex geometry. Dr. Gang Tian won Alan T. Waterman Award in 1994 and Veblen Prize in 1996. He spoke twice at the International Congress of Mathematics in 1990 and 2002. He was elected to the National Academy of China in 2001 and the American Academy of Arts and Science in 2004.