Prajwal Samal (IMPAN) - A tale of two Calabi-Yau 3-folds

I will present details about an ongoing joint work, where we intend to prove derived equivalence between two non-birational Calabi-Yau 3-folds. I will present a summary of the status of classification of CY3s and mirror symmetric motivations that prompt us to specifically study these two 3-folds. I will start with some classical projective geometry where we construct the titular 3-folds, following which I will move on to toric geometry where we showcase preliminary evidence for their derived equivalence. I will end with a discussion of GLSMs which is a relatively modern technique in the landscape of derived categories, which we hope will lead us to our desired proof.