Project acronym KAPIBARA
Project Homotopy Theory of Algebraic Varieties and Wild Ramification
Researcher (PI) Piotr ACHINGER
Host Institution (HI) INSTYTUT MATEMATYCZNY POLSKIEJ AKADEMII NAUK
Call Details Starting Grant (StG), PE1, ERC-2018-STG
Summary The aim of the proposed research is to study the homotopy theory of algebraic varieties and other algebraically defined geometric objects, especially over fields other than the complex numbers. A noticeable emphasis will be put on fundamental groups and on K(pi, 1) spaces, which serve as building blocks for more complicated objects. The most important source of both motivation and methodology is my recent discovery of the K(pi, 1) property of affine schemes in positive characteristic and its relation to wild ramification phenomena.
The central goal is the study of etale homotopy types in positive characteristic, where we hope to use the aforementioned discovery to yield new results beyond the affine case and a better understanding of the fundamental group of affine schemes. The latter goal is closely tied to Grothendieck's anabelian geometry program, which we would like to extend beyond its usual scope of hyperbolic curves.
There are two bridges going out of this central point. The first is the analogy between wild ramification and irregular singularities of algebraic integrable connections, which prompts us to translate our results to the latter setting, and to define a wild homotopy type whose fundamental group encodes the category of connections.
The second bridge is the theory of perfectoid spaces, allowing one to pass between characteristic p and p-adic geometry, which we plan to use to shed some new light on the homotopy theory of adic spaces. At the same time, we address the related question: when is the universal cover of a p-adic variety a perfectoid space? We expect a connection between this question and the Shafarevich conjecture and varieties with large fundamental group.
The last part of the project deals with varieties over the field of formal Laurent series over C, where we want to construct a Betti homotopy realization using logarithmic geometry. The need for such a construction is motivated by certain questions in mirror symmetry.
Summary
The aim of the proposed research is to study the homotopy theory of algebraic varieties and other algebraically defined geometric objects, especially over fields other than the complex numbers. A noticeable emphasis will be put on fundamental groups and on K(pi, 1) spaces, which serve as building blocks for more complicated objects. The most important source of both motivation and methodology is my recent discovery of the K(pi, 1) property of affine schemes in positive characteristic and its relation to wild ramification phenomena.
The central goal is the study of etale homotopy types in positive characteristic, where we hope to use the aforementioned discovery to yield new results beyond the affine case and a better understanding of the fundamental group of affine schemes. The latter goal is closely tied to Grothendieck's anabelian geometry program, which we would like to extend beyond its usual scope of hyperbolic curves.
There are two bridges going out of this central point. The first is the analogy between wild ramification and irregular singularities of algebraic integrable connections, which prompts us to translate our results to the latter setting, and to define a wild homotopy type whose fundamental group encodes the category of connections.
The second bridge is the theory of perfectoid spaces, allowing one to pass between characteristic p and p-adic geometry, which we plan to use to shed some new light on the homotopy theory of adic spaces. At the same time, we address the related question: when is the universal cover of a p-adic variety a perfectoid space? We expect a connection between this question and the Shafarevich conjecture and varieties with large fundamental group.
The last part of the project deals with varieties over the field of formal Laurent series over C, where we want to construct a Betti homotopy realization using logarithmic geometry. The need for such a construction is motivated by certain questions in mirror symmetry.
Max ERC Funding
1 007 500 €
Duration
Start date: 2019-06-01, End date: 2024-05-31
Project acronym STIMUNO
Project Searching for novel strategies improving cancer immunotherapy
Researcher (PI) Magdalena WINIARSKA
Host Institution (HI) WARSZAWSKI UNIWERSYTET MEDYCZNY
Call Details Starting Grant (StG), LS4, ERC-2018-STG
Summary The main goal of this project is to explore new fundamental pathways involved in the regulation of antitumor immune response. Since the immunosuppressive tumor microenvironment constitutes a key barrier to effective immunotherapy, our predominant ambition is to characterize novel, hitherto unknown metabolic changes that can support the survival of tumor cells and the escape from the immune surveillance.
We have recently discovered a new metabolite within tumor microenvironment with a robust ability to inhibit the activity of immune cells and their potential to kill target tumor cells. Within the project, we plan to corroborate on our preliminary findings in order to establish the role of this factor in mitigating antitumor immune response. To this end, we will determine the level of its production within tumors in murine models. Moreover, we will relate these findings to human data by analysing the immune milieu and the expression of enzymes involved in generation of this metabolic agent in a cohort of cancer patients. We will also investigate the mechanisms by which this factor could perturb the functions of tumor-infiltrating effector cells.
Finally, we aspire to use the knowledge gained during the implementation of this project to propose innovative therapeutic solutions. Specifically, we will investigate whether and how the inhibition of selected enzymes involved in the generation of this new metabolic checkpoint can impact on the efficacy of immunotherapeutic agents, including immune checkpoint inhibitors, arginase inhibitors as well as adoptive therapy with CAR-T cells and CAR-NK cells. We strongly believe that by achieving the goals of our project we will make a significant step forward in order to develop and to design cutting-edge therapeutic strategies. These compelling solutions would further improve the efficacy of tumor immunotherapy, thus contributing to a breakthrough advance in cancer treatment.
Summary
The main goal of this project is to explore new fundamental pathways involved in the regulation of antitumor immune response. Since the immunosuppressive tumor microenvironment constitutes a key barrier to effective immunotherapy, our predominant ambition is to characterize novel, hitherto unknown metabolic changes that can support the survival of tumor cells and the escape from the immune surveillance.
We have recently discovered a new metabolite within tumor microenvironment with a robust ability to inhibit the activity of immune cells and their potential to kill target tumor cells. Within the project, we plan to corroborate on our preliminary findings in order to establish the role of this factor in mitigating antitumor immune response. To this end, we will determine the level of its production within tumors in murine models. Moreover, we will relate these findings to human data by analysing the immune milieu and the expression of enzymes involved in generation of this metabolic agent in a cohort of cancer patients. We will also investigate the mechanisms by which this factor could perturb the functions of tumor-infiltrating effector cells.
Finally, we aspire to use the knowledge gained during the implementation of this project to propose innovative therapeutic solutions. Specifically, we will investigate whether and how the inhibition of selected enzymes involved in the generation of this new metabolic checkpoint can impact on the efficacy of immunotherapeutic agents, including immune checkpoint inhibitors, arginase inhibitors as well as adoptive therapy with CAR-T cells and CAR-NK cells. We strongly believe that by achieving the goals of our project we will make a significant step forward in order to develop and to design cutting-edge therapeutic strategies. These compelling solutions would further improve the efficacy of tumor immunotherapy, thus contributing to a breakthrough advance in cancer treatment.
Max ERC Funding
1 498 750 €
Duration
Start date: 2019-03-01, End date: 2024-02-29
