Ben Grant
@bengrantmath.bsky.social
PhD candidate in math at UConn. Interested in cluster algebras, representation theory, algebraic combinatorics, dimer models, knot theory, and logic. he/him/his
https://sites.google.com/view/benjamingrant
https://sites.google.com/view/benjamingrant
Reposted by Ben Grant
Scott Carter, Benjamin Cooper, Mikhail Khovanov, Vyacheslav Krushkal: An Extension of Khovanov Homology to Immersed Surface Cobordisms https://arxiv.org/abs/2510.14760 https://arxiv.org/pdf/2510.14760 https://arxiv.org/html/2510.14760
October 17, 2025 at 6:38 AM
Scott Carter, Benjamin Cooper, Mikhail Khovanov, Vyacheslav Krushkal: An Extension of Khovanov Homology to Immersed Surface Cobordisms https://arxiv.org/abs/2510.14760 https://arxiv.org/pdf/2510.14760 https://arxiv.org/html/2510.14760
Learned a really neat trick yesterday for a select family of competition-style problems with certain kinds of functional equations over the integers. As an example, suppose we’re tasked with finding all functions f:Z—>Z such that f(f(x))-4f(x)+3x=8 for all x. The trick is to turn this into a problem
October 16, 2025 at 1:52 AM
Learned a really neat trick yesterday for a select family of competition-style problems with certain kinds of functional equations over the integers. As an example, suppose we’re tasked with finding all functions f:Z—>Z such that f(f(x))-4f(x)+3x=8 for all x. The trick is to turn this into a problem
Reposted by Ben Grant
New blog post! Through a sequence of images, I verify that the unknotting number of the connected sum of a (2,7) torus knot and its mirror is less than 6: I show that this first image is the connected sum, and after changing those crossings, it produces the unknot! divisbyzero.com/2025/10/08/t...
October 9, 2025 at 3:00 AM
New blog post! Through a sequence of images, I verify that the unknotting number of the connected sum of a (2,7) torus knot and its mirror is less than 6: I show that this first image is the connected sum, and after changing those crossings, it produces the unknot! divisbyzero.com/2025/10/08/t...
Reposted by Ben Grant
from now on I'm just going to truncate the taylor series for sin at the first term. sin(x) = 0 for all x. this approximation
- is efficient to compute
- has bounded error
- has excellent analytic properties
- has very high accuracy for small values, which occur frequently in applications
- is efficient to compute
- has bounded error
- has excellent analytic properties
- has very high accuracy for small values, which occur frequently in applications
October 8, 2025 at 5:21 PM
from now on I'm just going to truncate the taylor series for sin at the first term. sin(x) = 0 for all x. this approximation
- is efficient to compute
- has bounded error
- has excellent analytic properties
- has very high accuracy for small values, which occur frequently in applications
- is efficient to compute
- has bounded error
- has excellent analytic properties
- has very high accuracy for small values, which occur frequently in applications
Very mild rant. GRFP reviews from last year’s application cycle came out a couple days ago. I applied last year but did not receive the award or an honorable mention (oh well, this happens, not the part that’s frustrating). Two of the three reviewers assigned to my application left very positive,
October 4, 2025 at 12:30 PM
Very mild rant. GRFP reviews from last year’s application cycle came out a couple days ago. I applied last year but did not receive the award or an honorable mention (oh well, this happens, not the part that’s frustrating). Two of the three reviewers assigned to my application left very positive,
Reposted by Ben Grant
Daniel Labardini Fragoso: Derksen-Weyman-Zelevinsky mutations of infinite-dimensional modules I: Foundations https://arxiv.org/abs/2508.21757 https://arxiv.org/pdf/2508.21757 https://arxiv.org/html/2508.21757
September 1, 2025 at 6:40 AM
Daniel Labardini Fragoso: Derksen-Weyman-Zelevinsky mutations of infinite-dimensional modules I: Foundations https://arxiv.org/abs/2508.21757 https://arxiv.org/pdf/2508.21757 https://arxiv.org/html/2508.21757
Reposted by Ben Grant
arxiv.org/abs/2508.20226
/Decompositions of augmentation varieties via weaves and rulings/
Johan Asplund, Orsola Capovilla-Searle, James Hughes, Caitlin Leverson, Wenyuan Li, Angela Wu
/Decompositions of augmentation varieties via weaves and rulings/
Johan Asplund, Orsola Capovilla-Searle, James Hughes, Caitlin Leverson, Wenyuan Li, Angela Wu
Decompositions of augmentation varieties via weaves and rulings
The braid variety of a positive braid and the augmentation variety of a Legendrian link both admit decompositions coming from weaves and rulings, respectively. We prove that these decompositions agree under an isomorphism between the braid variety and the augmentation variety. We also prove that both decompositions coincide with a Deodhar decomposition and another decomposition coming from the microlocal theory of sheaves. Our proof relies on a detailed comparison between weaves and Morse complex sequences. Among other things, we show that the cluster variables of the maximal cluster torus of the augmentation variety can be computed from the Legendrian via Morse complex sequences.
arxiv.org
August 29, 2025 at 2:02 AM
arxiv.org/abs/2508.20226
/Decompositions of augmentation varieties via weaves and rulings/
Johan Asplund, Orsola Capovilla-Searle, James Hughes, Caitlin Leverson, Wenyuan Li, Angela Wu
/Decompositions of augmentation varieties via weaves and rulings/
Johan Asplund, Orsola Capovilla-Searle, James Hughes, Caitlin Leverson, Wenyuan Li, Angela Wu
Man the lyricism here is something (excellent, beautiful song). I wouldn’t joke about this, I’m not kidding this time
August 29, 2025 at 12:55 AM
Man the lyricism here is something (excellent, beautiful song). I wouldn’t joke about this, I’m not kidding this time
Burn OpenAI to the ground.
August 26, 2025 at 11:14 PM
Burn OpenAI to the ground.
Reposted by Ben Grant
Registration for the SUBgroups program for first-year math grad students is now open!
Find out more and register here: gradsubgroups.org
Please share with any first-year math grad students you know who are looking for some regular peer support!
Find out more and register here: gradsubgroups.org
Please share with any first-year math grad students you know who are looking for some regular peer support!
SUBgroups
Online peer groups for first-year math graduate students.
gradsubgroups.org
August 26, 2025 at 7:16 PM
Registration for the SUBgroups program for first-year math grad students is now open!
Find out more and register here: gradsubgroups.org
Please share with any first-year math grad students you know who are looking for some regular peer support!
Find out more and register here: gradsubgroups.org
Please share with any first-year math grad students you know who are looking for some regular peer support!
If I had a dollar for every time, I would have uncountably many dollars
August 26, 2025 at 10:13 PM
If I had a dollar for every time, I would have uncountably many dollars
Reposted by Ben Grant
Roger Casals, Pavel Galashin, Mikhail Gorsky, Linhui Shen, Melissa Sherman-Bennett, Jos\'e Simental
Comparing cluster algebras on braid varieties
https://arxiv.org/abs/2508.03816
Comparing cluster algebras on braid varieties
https://arxiv.org/abs/2508.03816
August 7, 2025 at 5:45 AM
Roger Casals, Pavel Galashin, Mikhail Gorsky, Linhui Shen, Melissa Sherman-Bennett, Jos\'e Simental
Comparing cluster algebras on braid varieties
https://arxiv.org/abs/2508.03816
Comparing cluster algebras on braid varieties
https://arxiv.org/abs/2508.03816
Good feeling when you come up with a research question that (1) you have no idea how to tackle and (2) the answer is going to be interesting, no matter what it is
August 6, 2025 at 2:03 AM
Good feeling when you come up with a research question that (1) you have no idea how to tackle and (2) the answer is going to be interesting, no matter what it is
Reposted by Ben Grant
the USA built a system of higher education so good that smart/rich people from across the world came here, spending billions to learn here, subsidizing education for Americans while spending money to live in our cities and towns. our government arbitrarily decided we should stop doing that
The US could see a 30-40% decline in new international student enrollment, resulting in nearly $7 billion in lost revenue and more than 60,000 fewer American jobs. https://www.nafsa.org/fall-2025-international-student-enrollment-outlook-and-economic-impact
August 3, 2025 at 3:39 PM
the USA built a system of higher education so good that smart/rich people from across the world came here, spending billions to learn here, subsidizing education for Americans while spending money to live in our cities and towns. our government arbitrarily decided we should stop doing that
Reposted by Ben Grant
Andrew DeLapo, David Gonzalez
Computability of Separation Axioms in Countable Second Countable Spaces
https://arxiv.org/abs/2507.18564
Computability of Separation Axioms in Countable Second Countable Spaces
https://arxiv.org/abs/2507.18564
July 25, 2025 at 4:20 AM
Andrew DeLapo, David Gonzalez
Computability of Separation Axioms in Countable Second Countable Spaces
https://arxiv.org/abs/2507.18564
Computability of Separation Axioms in Countable Second Countable Spaces
https://arxiv.org/abs/2507.18564
“Completely forkless quivers” sir this is a Dairy Queen
July 25, 2025 at 5:54 AM
“Completely forkless quivers” sir this is a Dairy Queen
Reposted by Ben Grant
The two largest pediatric care centers in deep blue Connecticut have stopped providing gender affirming care to minors.
ctmirror.org/2025/07/24/y...
ctmirror.org/2025/07/24/y...
Yale New Haven Health to cut youth gender-affirming care services
News that YNHH will no longer provide medication for gender-affirming care services comes a day after a similar announcement from CCMC.
ctmirror.org
July 24, 2025 at 8:46 PM
The two largest pediatric care centers in deep blue Connecticut have stopped providing gender affirming care to minors.
ctmirror.org/2025/07/24/y...
ctmirror.org/2025/07/24/y...
Reposted by Ben Grant
"Abolish ICE" needs to be the centrist Democratic position going forward. The leftist position is "Charge everyone involved in this with war crimes." www.theguardian.com/us-news/2025...
Migrants at Ice jail in Miami made to kneel to eat ‘like dogs’, report alleges
Incident in which migrants were shackled with hands tied one of succession of alleged abuses at jails in Florida
www.theguardian.com
July 21, 2025 at 9:40 PM
"Abolish ICE" needs to be the centrist Democratic position going forward. The leftist position is "Charge everyone involved in this with war crimes." www.theguardian.com/us-news/2025...
Reposted by Ben Grant
I don't think mathematicians who use or promote LLMs are, on the whole, worried enough about the extent this applies to them
It does seem like a problem that these tools depend on humans to create new information that they can regurgitate and that they’re creating the economic conditions that will make those people even rarer than they already are
July 19, 2025 at 5:22 PM
I don't think mathematicians who use or promote LLMs are, on the whole, worried enough about the extent this applies to them
Reposted by Ben Grant
POLITICS IS NOT A SPORT. YOU DON'T ACTUALLY HAVE TO COVER POLITICS LIKE IT'S ALL A BIG GAME.
"Trump is at the top of his game right now," says our Capitol bureau chief and senior Washington columnist Rachael Bade.
Watch Bade break down his four biggest wins of the past two weeks and read her column about how he dominated Congress here 👇
ow.ly/XJWA50WkI3k
Watch Bade break down his four biggest wins of the past two weeks and read her column about how he dominated Congress here 👇
ow.ly/XJWA50WkI3k
July 3, 2025 at 9:14 PM
POLITICS IS NOT A SPORT. YOU DON'T ACTUALLY HAVE TO COVER POLITICS LIKE IT'S ALL A BIG GAME.
Reposted by Ben Grant
I don’t think anyone is prepared for what they just did w/ ICE.
This is not a simple budget increase. It is an explosion - making ICE bigger than the FBI, US Bureau of Prisons, DEA,& others combined.
It is setting up to make what’s happening now look like child’s play. And people are disappearing.
This is not a simple budget increase. It is an explosion - making ICE bigger than the FBI, US Bureau of Prisons, DEA,& others combined.
It is setting up to make what’s happening now look like child’s play. And people are disappearing.
July 3, 2025 at 6:58 PM
I don’t think anyone is prepared for what they just did w/ ICE.
This is not a simple budget increase. It is an explosion - making ICE bigger than the FBI, US Bureau of Prisons, DEA,& others combined.
It is setting up to make what’s happening now look like child’s play. And people are disappearing.
This is not a simple budget increase. It is an explosion - making ICE bigger than the FBI, US Bureau of Prisons, DEA,& others combined.
It is setting up to make what’s happening now look like child’s play. And people are disappearing.
This man is a political talent
I'm proud I don't have Andrew Cuomo's record of corruption, scandal and disgrace.
And the name is M-A-M-D-A-N-I.
And the name is M-A-M-D-A-N-I.
June 13, 2025 at 12:53 AM
This man is a political talent
Reposted by Ben Grant
At this point, I would suggest as a general rule that the greater the embrace of this kind of approach to generative AI, the less invested the institution is in students actually learning something or having genuinely meaningful experiences. Students beware. www.nytimes.com/2025/06/07/t...
Welcome to Campus. Here’s Your ChatGPT.
www.nytimes.com
June 7, 2025 at 12:12 PM
At this point, I would suggest as a general rule that the greater the embrace of this kind of approach to generative AI, the less invested the institution is in students actually learning something or having genuinely meaningful experiences. Students beware. www.nytimes.com/2025/06/07/t...
Reposted by Ben Grant
Spent a lot of this week doing the kind of slow research/writing/thinking where I’m really trying to figure stuff out and I can’t emphasize enough how multitasking is incompatible with this kind of work
June 6, 2025 at 9:51 PM
Spent a lot of this week doing the kind of slow research/writing/thinking where I’m really trying to figure stuff out and I can’t emphasize enough how multitasking is incompatible with this kind of work
Possibly a hot take, but one that I have been aggressively forced into by a problem I’m working on: Reidemeister II moves are more difficult to deal with than Reidemeister III moves
June 4, 2025 at 8:44 AM
Possibly a hot take, but one that I have been aggressively forced into by a problem I’m working on: Reidemeister II moves are more difficult to deal with than Reidemeister III moves