Calendar
- 06September 6, 2022
CMSA Active Matter: State Diagram of Cancer Cell Unjamming Predicts Metastatic Risk
Distant metastasis is probably the most lethal hallmark of cancer. Due to a lack of suitable markers, cancer cell motility only has a negligible impact on current diagnosis. Based on cell unjamming we derive a cell motility marker for static histological images. This enables us to sample huge numbers of breast cancer patient data to derive a comprehensive state diagram of unjamming as a collective transition in cell clusters of solid tumors. As recently discovered, cell unjamming transitions occur in embryonic development and as pathological changes in diseases such as cancer. No consensus has been achieved on the variables and the parameter space that describe this transition. Cell shapes or densities based on different unjamming models have been separately used to describe the unjamming transition under different experimental conditions. Moreover, the role of the nucleus is not considered in the current unjamming models. Mechanical stress propagating through the tissue mechanically couples the cell nuclei mediated by the cell’s cytoplasm, which strongly impacts jamming.Based on our exploratory retrospective clinical study with N=1,380 breast cancer patients and vital cell tracking in patient-derived tumor explants, we find that the unjamming state diagram depends on cell and nucleus shapes as one variable and the nucleus number density as the other that measures the cytoplasmic spacing between the nuclei. Our approach unifies previously controversial results into one state diagram. It spans a broad range of states that cancer cell clusters can assume in a solid tumor. We can use an empirical decision boundary to show that the unjammed regions in the diagram correlate with the patient’s risk for metastasis.We conclude that unjamming within primary tumors is part of the metastatic cascade, which significantly advances the understanding of the early metastatic events. With the histological slides of two independent breast cancer patients’ collectives, we train (N=688) and validate (N=692) our quantitative prognostic index based on unjamming regarding metastatic risk. Our index corrects for false high- and low-risk predictions based on the invasion of nearby lymph nodes, the current gold standard. Combining information derived from the nodal status with unjamming may reduce over- and under-treatment.For more information on how to join, please see: https://cmsa.fas.harvard.edu/active-matter-seminar/
- 07September 7, 2022
Informal Seminar: Exotic homeomorphisms and flows (after Sullivan and Freedman)
Science Center 5071 Oxford Street, Cambridge, MA 02138 USAFor more information, please see: https://math.harvard.edu/~ctm/sem
- 07September 7, 2022
CMSA Quantum Matter in Mathematics and Physics: Gifts from anomalies: new results on quantum critical transport in non-Fermi liquids
Non-Fermi liquid phenomena arise naturally near Landau ordering transitions in metallic systems. Here, we leverage quantum anomalies as a powerful nonperturbative tool to calculate optical transport in these models in the infrared limit. While the simplest such models with a single boson flavor (N=1) have zero incoherent conductivity, a recently proposed large N deformation involving flavor-random Yukawa couplings between N flavors of bosons and fermions admits a nontrivial incoherent conductivity (z is the boson dynamical exponent) when the order parameter is odd under inversion. The presence of incoherent conductivity in the random flavor model is a consequence of its unusual anomaly structure. From this we conclude that the large N deformation does not share important nonperturbative features with the physical N = 1 model, though it remains an interesting theory in its own right. Going beyond the IR fixed point, we also consider the effects of irrelevant operators and show, within the scope of the RPA expansion, that the old result
due to Kim et al. is incorrect for inversion-odd order parameters.
For more information on how to join, please see: https://cmsa.fas.harvard.edu/quantum-matter-seminar/
- 10September 10, 2022
Diving Into Math with Emmy Noether
Diving Into Math with Emmy Noether
A theatre performance about the life of one of history’s most influential mathematicians.
When: Saturday, September 10, 2022
Panel Discussion: 4:30 p.m. – 5 p.m. | Play: 5:15 p.m. | Reception: 6:30 p.m. – 7:30 p.m.
Where: Harvard University Hilles Cinema, Student Organization Center at Hilles (SOCH)
59 Shepard Street, Cambridge, MA 02138
Panelists:
- Melissa Franklin | Harvard University Mallinckrodt Professor of Physics
- Barry Mazur | Harvard University Gerhard Gade University Professor
- Monica Noether | Vice President, Charles River Associates | Grandniece of Emmy Noether
- David Rowe | Mainz University Professor
Unfortunately, as of right now venue capacity has been reached. If you’d like to sign up to be waitlisted, please register below and we will inform you by Friday, September 9 if seats become available.
Waitlist Registration
Emmy Noether (1882-1935) was one of the most influential mathematicians of the last century. Her works and teachings left a lasting mark on modern algebra, opening new avenues for a modern structural perspective in mathematics.
The ensemble Portraittheater Vienna (Austria) together with the Frei Universität Berlin (Germany) produced a biographical play about Emmy Noether, directed by Sandra Schüddekopf and starring Anita Zieher as Emmy. In September 2022, “Diving into Math with Emmy Noether” will tour the USA for the first time and play at several universities and colleges. The Harvard Department of Mathematics and the Center of Mathematical Sciences and Applications (CMSA) are proud to bring this performance to Harvard University.
Based on historical documents and other sources, the script was written by Sandra Schüddekopf and Anita Zieher in cooperation with the historians Mechthild Koreuber and David E. Rowe. On stage and in videos, Emmy Noether’s fascinating personality comes alive in her reflections and conversations with other leading mathematicians of her day. The original play in German has been performed with great success at several universities in Germany and in the Theater Drachengasse in Vienna.
A coproduction by portraittheater Vienna and Freie Universität Berlin. Scientific Board: Mechthild Koreuber, David Rowe.
- 13September 13, 2022
Harvard/MIT Algebraic Geometry Seminar: Dynamical moduli spaces of linear maps with marked points
Science Center 5071 Oxford Street, Cambridge, MA 02138 USAModuli spaces of degree d dynamical systems on projective space are fundamental in algebraic dynamics. When the degree d is at least 2, these moduli spaces can be defined via geometric invariant theory (GIT), but when d = 1, there are no GIT stable linear maps. Inspired by the case of genus 0 curves, we show how to recover a nice moduli space by including marked points. Linear maps are the simplest dynamical systems, but with marked points, the moduli space becomes quite subtle. We construct the moduli space of linear maps with marked points, prove its rationality, and show that GIT stability is characterized by subtle dynamical conditions on the marked map related to Hessenberg varieties. The proof is a combinatorial analysis of polytopes generated by root vectors of the A_N lattice from Lie theory.