##### Overview

We are organizing a Macaulay2 conference at Cleveland State University in Cleveland, OH from Friday, May 27 to Sunday, May 29, 2022 (conference activities running from Friday afternoon through Sunday morning).

The main goal of the conference is to showcase state-of-the-art research in computational commutative algebra, algebraic geometry, and related areas, including (but not limited to) work resulting from the 2020 M2@CSU workshop. In addition, we hope the conference will provide an ideal forum for the exchange of mathematical ideas in our community. In order to facilitate social interactions among colleagues, we will focus primarily on in-person participation; however, we also plan to stream talks on Zoom (please contact the organizers for the link).

For planning purposes, we kindly request all interested participants to register here. NSF funding will provide partial support for travel and lodging (priority will go to graduate students, postdocs, and participants from underrepresented communities). If you wish to apply for this kind of support, we ask that you submit your application by January 31, 2022.##### Internals meeting

##### Code of Conduct

- All visitors to campus must adhere to applicable CSU policies. Notice in particular the CSU policy against discrimination, harassment, sexual violence, and retaliation.
- We are dedicated to providing a harassment-free conference experience for everyone, regardless of gender, gender identity and expression, age, sexual orientation, disability, physical appearance, race, ethnicity, national origin, or religion (or lack thereof). We do not tolerate harassment of conference participants in any form. Any incidents may be reported to the organizers or CSU police.
- Effective May 21, 2022, masking on the CSU campus is optional, and there are no social distancing requirements. Conference participants are welcome to wear masks, and we ask that all attendees respect the choices of other people on campus. The CDC recommends that COVID-positive individuals isolate at home for 5 days after symptoms develop, and wear a mask for an additional 5 days when returning to public places. Please check the CSU COVID-19 safety protocols for updates before coming to campus.

##### Venue and Local Information

- Conference events will take place in Berkman Hall 445 on the Cleveland State University campus at 2121 Euclid Avenue, Cleveland, OH. Accessible entrance and elevators are located at the corner of East 22nd Street and Chester Avenue.
- The Internals workshop will take place in Rhodes Tower 1402. Accessible entrance to Rhodes Tower is available from Euclid Avenue (around or through the Student Center, then across the plaza), and from the garage level on East 21st or East 22nd Street.
- Here is a campus map and a map of parking locations.
- Here is some accessibility information for visitors to the CSU campus.
- Inclusive multi-stall restrooms are located in front of the conference room, and more restrooms are available on the same floor closer to the center of the building. Here is a list of gender neutral restrooms on campus.
- Internet access for campus visitors is provided by Eduroam or by the (unsecured) CSUguest network.
- The map below shows some restaurants and coffee shops near the CSU campus. View it on Google Maps.

##### Speakers

(click name to expand)Abelian groups -- modules over the integers -- are well-described by giving generators and relations, conveniently described by one matrix of integers. For modules over a polynomial ring in n variables David Hilbert improved the description to one requiring n matrices, the "free resolution". But for most commutative rings, the corresponding description requires infinitely many matrices.

In the finite case, we know a lot, and in the first half of this talk I will survey some of what we've learned in the 130 years since Hilbert's work. But except for very special cases, we know almost nothing in the infinite case. In the second half of the talk I will introduce some new problems and conjectures that Hai Long Dao and I have been working on, with the help of the program Macaulay2.`InvariantRing`

package for *Macaulay2*. In addition to expanding and improving the methods of the existing package for actions of finite groups, the updated package adds functionality for computing invariants of diagonal actions of tori and finite abelian groups as well as invariants of arbitrary linearly reductive group actions. The implementation of the package has been completely overhauled with the aim of serving as a unified resource for invariant theory computations in

*Macaulay2*.