Liberty Global will be holding a Careers Insight Event on the 23rd October at 5pm in the Tanner Room in Linacre College. The EPSRC Centre for Doctoral Training in Quantum Informatics (QI CDT) invites applications for up to 16 fully funded four-year PhD studentships in Quantum Informatics with Integrated Study for September 2026 entry.
These PhDs will begin in September 2026, and the deadline to apply is 8th January 2026.
How to Apply
The LSE Department of Statistics PhD Open Day is on 11 November 2025. This event is designed for aspiring research students who are keen to learn more about studying a PhD in Statistics at LSE. It is also a fantastic opportunity to meet our faculty, current research students and alumni.The start of a new term can often be an overwhelming time. There's lots of resources for you within your College or across the wider university. Here in the Maths Institute, we want to support you as best we can.
The Maths Institute has a student-specific email that can act as a first point of call. If you have a question or concern and you're not sure who to ask, email @email.
Special Lunch Pop-Up: Poke Bowls
Tuesday, 21 October 12 pm – 2 pm
Our fresh, flavourful poke bowls for only £6.50 - choose from Chicken Katsu or Kinoko Mushroom. Served with jasmine rice and your choice of toppings - pickled red cabbage, sweetcorn, edamame beans, and more.
Dash Water: free samples
Wednesday, 22 October 12 pm – 2 pm
Rothesay will be visiting the Maths Institute on Thursday 30th October. They will be in L4, delivering a presentation on Quantitative Strategy. All Part C, OMMS and MSc students are welcome to attend.
Quantitative Strategy at Rothesay
Calling all maths and finance Masters students! Are you ready to see how cutting-edge math shapes the world of finance? Join Rothesay’s Quantitative Strategist team for an exclusive event where theory meets real-world impact!
15:30
Descendent generating series for Pandharipande-Thomas stable pairs on Fano 3-folds
Abstract
We adapt Joyce's theory of wall-crossing for enumerative invariants of $\mathbb C$-linear additive categories to Pandharipande-Thomas stable pairs on smooth projective Fano 3-folds of "type C or D", and investigate implications for Pandharipande-Thomas generating functions with descendent insertions.
By analyzing the wall-crossing behavior from a stability condition where pairs are unstable to the standard stability condition for PT stable pairs, we derive an explicit formula expressing the PT stable pair invariants $[P_n(X,\beta)]^{virt}$ in terms of sheaf-theoretic invariants $[\mathcal M^{ss}_{(0,0,\beta_i, n_i - \beta_i.c_1/2)}(\tau_-)]_{\rm inv}$ for the moduli space of Gieseker semistable coherent sheaves on $X$ with Chern character $(0,0,\beta_i, n_i - \beta_i.c_1/2)$.
These enumerative invariants are defined as elements in the Lie algebra on the rational Betti homology of the piecewise-linear rigidified higher moduli stack of objects in the bounded derived category of X. Under tensoring by a line bundle, we exhibit a control over the periodicity of sheaf-theoretic invariants with respect to the Euler characteristic $n_i$, which we use to show that the sheaf-theoretic invariants form a quasi-polynomial in $n_i$ of degree $2$ with period given by the divisibility of $\beta_i$ in the lattice $H_2(X,\mathbb Z)/\text{torsion}$.
We use this periodicity in the sheaf-theoretic invariants to show that the descendent generating series for Pandharipande-Thomas stable pairs is the Laurent expansion of a rational function over $\mathbb Q$ in this setting, thus confirming a conjecture due to Pandharipande-Thomas from 2007. Furthermore, we construct a counterexample to a conjecture due to Pandharipande from 2017 on the location of the poles of the descendent generating series, and give a direct proof of a slightly modified conjecture on the location of these poles using wall-crossing techniques.