Recently, almost all conferences have moved to virtual mode due to the pandemic-induced restrictions on travel and social gathering. Contrary to in-person conferences, virtual conferences face the challenge of efficiently scheduling talks, accounting for the availability of participants from different timezones and their interests in attending different talks. A natural objective for conference organizers is to maximize efficiency, e.g., total expected audience participation across all talks. However, we show that optimizing for efficiency alone can result in an unfair virtual conference schedule, where individual utilities for participants and speakers can be highly unequal. To address this, we formally define fairness notions for participants and speakers, and derive suitable objectives to account for them. As the efficiency and fairness objectives can be in conflict with each other, we propose a joint optimization framework that allows conference organizers to design schedules that balance (i.e., allow trade-offs) among efficiency, participant fairness and speaker fairness objectives. While the optimization problem can be solved using integer programming to schedule smaller conferences, we provide two scalable techniques to cater to bigger conferences. Extensive evaluations over multiple real-world datasets show the efficacy and flexibility of our proposed approaches.