Theoretical/algorithmic tools from real algebraic geometry have been rigorously applied to the study of positive polynomials and the complexity analysis of semidefinite and polynomial optimization. Real algebraic geometry is the study of semi-algebraic subsets, which include the feasible sets of semidefinite and polynomial optimizationas special cases. Due to the existence of efficient interior-point methods, semidefinite optimization has been an emerging computational tool in polynomial optimization and quantum computing, with numerous applications in theoretical computer science, control theory, and statistics.

The goals behind organizing these seminars and sessions are to bring together a diverse group of experts from areas of optimization, commutative algebra, differential geometry, algebraic topology, and real/complex algebraic geometry. The main topics will include the topology of semi-algebraic set, the complexity aspects of real algebraic geometry, and their applications to optimization theory with special emphasis on semidefinite and polynomial optimization.

## Seminars

- 2022-2023, Carnegie Mellon University: Optimization, Algebra, and Geometry Seminar
- Spring 2022, Purdue University: Optimization and Real Algebraic Geometry Seminar

## Conferences and Special sessions

- Joint Mathematics Meetings 2023: Special session on Complexity and Topology in Computational Algebraic Geometry
- AMS Spring Central Sectional Meeting 2022, Virtual: Special Session on Optimization, Complexity, and Real Algebraic Geometry
- SIAM Conference on Applied Algebraic Geometry 2021, Virtual: Minisymposium on Algebraic Aspects of Optimization
- SIAM Conference on Optimization, Virtual: Minisymposium on Recent Advances in Semidefinite and Polynomial Optimization
- AMS Spring Southeastern Sectional Meeting 2021, Virtual: Special Session on Optimization and Real Algebraic Geometry
- Joint Mathematics Meetings 2021, Virtual: Special Session on Optimization and Algebraic Geometry