# Category: Geometry

## June 1 – 30, 2019 » Homological Algebra, Microlocal Analysis and Symplectic Geometry

## July 1 – 31, 2019 » Expansions, Lie Algebras and Invariants

## August 1 – 31, 2019 » Quiver Varieties and Representation Theory

**Organizers: Joel Kamnitzer (Toronto), Hugh Thomas (UQAM)**

The representation theory of quivers (and related preprojective algebras) has been studied by researchers from algebra, while the geometry of quiver varieties has been studied by researchers in geometric representation theory. This activity will bring together members of these two communities to exchange recent progress and to stimulate further research and collaboration. Among other topics, we will discuss quantization of quiver varieties, Coulomb branch constructions using quiver varieties, tilting theory for preprojective algebras, and categorification of cluster algebras.

Some funding is available for graduate students and young researchers. Funding requests should include a brief letter explaining your interest and level of funding needed, as well as a cv, and should be sent to jkamnitz@math.toronto.edu .

Students should also arrange for a letter of support to be sent by their supervisor. Requests must be received by February 28; in some cases, requests received earlier may be acted on earlier.

## September 1 – 30, 2019 » Low-Dimensional Topology

**Organizers: Steven Boyer (UQAM), Liam Watson (Sherbrooke)**

As part of the 50th anniversary program, the CRM will host a thematic month in low-dimensional topology (September 2019). This is an area of research that includes geometric topology in dimensions 3 and 4, knot theory, and geometric group theory (to name a few) while drawing on techniques from symplectic topology and gauge theory towards the resolution of long-standing problems. While many new connections are being established, the field as a whole is at an exciting crossroads; some of the greatest open problems have been resolved—such as the geometrization of 3-manifolds due to Perelman and the positive resolution of the virtual Haken conjecture due to Agol and Wise. These works have opened new vistas of questions and conjectures for further study.

The CRM is delighted that Ciprian Manolescu will serve as distinguished researcher-in-residence for the thematic month. Manolescu’s recent and highly celebrated disproof of the triangulation conjecture [Pin(2)-*equivariant Seiberg–Witten Floer homology and the triangulation conjecture*, Journal of the American Mathematical Society, 2016] is emblematic of the current activity in low-dimensions described above. Manolescu’s work develops gauge-theoretic tools that resolve low-dimensional problems known to be linked to the existence of triangulations in high dimensions. This has re-invigorated gauge theoretic methods in low-dimensions, as evidenced by a string of exciting work from Manolescu and his students.

The aim of this focused month, which will coalesce around the work of the program’s researcher-in-residence, will be to take stock of current developments in the field and highlight the many exciting new directions present in this area of research. As such, the program will endeavour to include and be accessible to early career researchers in low-dimensional topology and related fields,