Hello Quantum Formalists,

As we start 2023, I am excited to highlight some of the planned activities for the year below!

**Measure Theory & Functional Analysis (Second half): **The first half of the MTFA course (playlist here) covered the foundational notions of measure theory and integration theory. The second half will take us into the course's main objective, infinite-dimensional Hilbert spaces!

**Category Theory:** We're working on a short crash course on Category theory to be delivered by our friend Brian Hepler! The following is more or less the outline for the course:

Categories, Functors, and Naturality

Universal Properties and the Yoneda Lemma

Limits and Colimits

Adjoint Functors

"And Beyond" (applications to algebraic topology (e.g., persistent homology), representation theory, Abelian categories, Derived categories, Topos theory, etc.?)

When will the course start? Between the end of February and mid-March. Also, most likely before Lie Groups & Representations! Doing it before the Lie stuff will give you another powerful mathematical machinery you can use with the Lie stuff on your research projects.

**Lie Groups & Representations: **This will be the final module of the three-module course that includes the past crash courses on abstract Group Theory & Representations (playlist here) and Topology & Differential Geometry (playlist here).

**QF Microgrants (Invite Only): **In parallel with the QF mathematical mentorship program, we plan to run an open source Quantum computing proof of concept (PoC) microgrant (circa $5K - $10K) trial scheme next year. It is inspired by what the excellent team at Unitary Fund have been doing, but with a narrow focus on specific areas of intellectual curiosity to myself & colleagues at my company. We're particularly keen to see the application of advanced mathematical topics, where possible! Some areas of interest include; classical-to-quantum data encoding, distributed federated learning on NISQ devices (i.e. Federated QML on NISQ devices) and quantum error mitigation.

We'll provide both the grant (circa $5K -$10K) and PhD-level mathematicians to work with the grant recipients. Ideally, PoC projects should take around 3 - 6 months to complete, and we'll be flexible to give additional grants to the most promising projects! Also, although we welcome joint applications, a maximum of three people will be allowed per application.

If you would like to learn more and be invited to apply, please fill out the following form https://forms.gle/1T5Gs6JAeaGjmfG6A. Likewise, if you know anyone who could be interested, please share!

Thank you for your continued support, and I look forward to your feedback on the QF's 2023 activities highlighted above.

Bambordé