Media Release –
April 21, 2023
Canadian Mathematical Society |

# DR. TONI ANNALA NAMED 2023 CMS BLAIR SPEARMAN DOCTORAL PRIZE RECIPIENT

OTTAWA, ON – The Canadian Mathematical Society (CMS) is pleased to announce that Dr. Toni Annala (Institute for Advanced Study, Princeton) has been named the 2023 CMS Blair Spearman Doctoral Prize recipient. Dr. Annala is an exceptional researcher working at the interface of algebraic geometry and algebraic topology, focusing on the development of cohomology theories using derived techniques. During his doctoral studies at the University of British Columbia (2017-2020, 2022), where he worked under the mentorship of Dr. Kalle Karu, Annala wrote more than 10 original research articles — of which more than half are single author. Across his thesis and these articles, almost all of which are now published or accepted in excellent journals such as Annales de l’Institut Fourier, Journal of the European Mathematical Society, and Advances in Mathematics, Annala has made significant contributions to an emerging theory of derived algebraic cobordism.

In most branches of geometry and topology, mathematicians seek meaningful, computable invariants that can be used to decide when two spaces are distinct from one another from the perspective of some natural notion of equivalence. The invariants at play and the notions of equivalence are generally dictated by the level of structure enjoyed by the spaces — for instance, they may simply be topological spaces or they may be endowed with the structure of algebraic varieties over some field. They may also be smooth or singular, and this distinction often leads to significant leaps in the difficulty faced in defining invariants. Homology and cohomology are ubiquitous sources of invariants, taking on various flavours such as Chow theory and K-theory. A generalized cohomology theory that is in some sense universal amongst these is that of algebraic cobordism. It is the algebraic or motivic analogue of complex cobordism for smooth schemes (of quasi-projective type) over a field. In his thesis and papers, Annala significantly extends a deep sequence of existing work on Chow theory, K-theory, and algebraic cobordism theory, including results of Voevodsky, Fulton-MacPherson, Levine-Morel, and Levine-Pandharipande. One of the key challenges motivating this sequence of investigations has been to define bivariant versions of Chow theory and K-theory on singular varieties that include both a homology and a cohomology, so that classes can be multiplied or intersected. Annala’s contribution to these works is a sweeping one: he has produced a bivariant cobordism theory, the cohomology of which generalizes the cohomology of the bivariant K-theory of Fulton-MacPherson and providing a candidate for a Chow cohomology theory, which has been open for some time.

To achieve this, Annala has made careful and deep investigations into derived algebraic geometry. Through associated techniques, he has been able to remove some restrictions in the prior work of others, such as the need for a certain homotopy invariance required to produce geometric descriptions of Grothendieck groups of vector bundles on schemes. One referee remarks that Annala’s thesis work is “more on the level of a German Habilitation presented by an experienced researcher than what one might expect from a doctoral student. The work presented here has already had a significant impact on this area of research and has received corresponding international attention.”

We also recognize that Annala, in parallel to his work in algebraic geometry, has been active in other areas of mathematics and science, such as topological aspects of condensed matter physics and the development of quantum algorithms, leading to further publications. His ability to pursue these investigations in parallel and with great success speaks to Annala’s remarkable independence as a graduate student. Taken all together, Annala’s works are suggestive of a broad vision for geometry, algebra, topology, and computation in mathematics and science. We foresee further groundbreaking work from Dr. Annala in the years to come.

**About the CMS Blair Spearman Doctoral Prize**

The CMS Blair Spearman Doctoral Prize recognizes outstanding performance by a doctoral student. The prize is awarded to one or two recipients of a Ph.D. from a Canadian university whose overall performance in graduate school is judged to be the most outstanding. Although the dissertation will be the most important criterion (the impact of the results, the creativity of the work, the quality of exposition, etc.) it will not be the only one. Other publications, activities in support of students and other accomplishments will also be considered.

For more information, visit the CMS Blair Spearman Doctoral Prize page.

**About the Canadian Mathematical Society (CMS)**

The CMS is the main national organization whose goal is to promote and advance the discovery, learning and application of mathematics. The Society’s activities cover the whole spectrum of mathematics including: scientific meetings, research publications, and the promotion of excellence in mathematics competitions that recognize outstanding student achievements.

**For more information, please contact:**

Dr. Termeh Kousha Executive Director Canadian Mathematical Society tkousha@cms.math.ca |
or |
Dr. Andrew Granville (Université de Montréal) Chair, Doctoral Prize Selection Committee Canadian Mathematical Society chair-resc@cms.math.ca |